对数函数的运算公式.

运算法则公式如下：1、lnx+ lny=lnxy2、lnx-lny=ln(x/y)3、lnxu207f=nlnx4、ln(u207f√x)=lnx/n5、lne=1对数公式是数学中的一种常见公式，如果a^x=N(a>0，且a≠1)，则x叫做以a为底N的对数，记做x=log(a)(N)，其中a要写于log右下。其中a叫做对数的底，N叫做真数。通常将以10为底的对数叫做常用对数，以e为底的对数称为自然对数。对数运算，实际上也就是指数在运算。应用对数在数学内外有许多应用。这些事件中的一些与尺度不变性的概念有关。例如，鹦鹉螺的壳的每个室是下一个的大致副本，由常数因子缩放。这引起了对数螺旋。Benford关于领先数字分配的定律也可以通过尺度不变性来解释。对数也与自相似性相关。例如，对数算法出现在算法分析中，通过将算法分解为两个类似的较小问题并修补其解决方案来解决问题。以上内容参考：百度百科-对数

对数函数公式是：loga(MN)=logaM+logaNloga(M/N)=logaM-logaNlogaNn=nlogaN(n,M,N∈R)如果a=em，则m为数a的自然对数，即lna=m，e=2.718281828…为自然对数的底，其为无限不循环小数。定义：若an=b（a>0，a≠1）则n=logab。log在高中数学里表示对数。一般地，函数y=logax（a>0，且a≠1）叫做对数函数，也就是说以幂（真数）为自变量，指数为因变量，底数为常量的函数，叫对数函数。通常我们将以10为底的对数叫常用对数（common logarithm），并把log10N记为lgN。另外，在科学计数中常使用以无理数e=2.71828......为底数的对数，以e为底的对数称为自然对数（natural logarithm），并且把logeN 记为In N。

对数基本恒等式：a^log_a_N=N 积的对数等于对数的和log(MN)=logM+logN 省略底数a 商的对数等于对数的差log(M/N)=logM-logN 幂的对数等于对数的对数乘指数log(N^m)=mlogN 根式的对数等于被开方数的对数除以根指数log[N^(1/n)]=(1/n)logN对数的换底公式：log_b_N=log_a_N/log_a_b

(1)性质①loga(1)=0；②loga(a)=1；③负数与零无对数.④log(0)=1(2)运算法则　　①loga(MN)=logaM+logaN；　　②loga(M/N)=logaM－logaN；　　③对logaM中M的n次方有=nlogaM；　　如果a=e^m，则m为数a的自然对数，即lna=m，e=2.718281828…为自然对数的底。3)换底公式　　logaN=(logmN)/(logma)(4)推导公式　　log(1/a)(1/b)=loga(b)　　loga(b)*logb(a)=1

对数的性质及推导用^表示乘方，用log(a)(b)表示以a为底，b的对数*表示乘号，/表示除号定义式：若a^n=b(a>0且a≠1)则n=log(a)(b)基本性质：1.a^(log(a)(b))=b2.log(a)(MN)=log(a)(M)+log(a)(N);3.log(a)(M/N)=log(a)(M)-log(a)(N);4.log(a)(M^n)=nlog(a)(M)推导1.这个就不用推了吧，直接由定义式可得(把定义式中的[n=log(a)(b)]带入a^n=b)2.MN=M*N由基本性质1(换掉M和N)a^[log(a)(MN)] = a^[log(a)(M)] * a^[log(a)(N)]由指数的性质a^[log(a)(MN)] = a^{[log(a)(M)] + [log(a)(N)]}又因为指数函数是单调函数，所以log(a)(MN) = log(a)(M) + log(a)(N)3.与2类似处理MN=M/N由基本性质1(换掉M和N)a^[log(a)(M/N)] = a^[log(a)(M)] / a^[log(a)(N)]由指数的性质a^[log(a)(M/N)] = a^{[log(a)(M)] - [log(a)(N)]}又因为指数函数是单调函数，所以log(a)(M/N) = log(a)(M) - log(a)(N)4.与2类似处理M^n=M^n由基本性质1(换掉M)a^[log(a)(M^n)] = {a^[log(a)(M)]}^n由指数的性质a^[log(a)(M^n)] = a^{[log(a)(M)]*n}又因为指数函数是单调函数，所以log(a)(M^n)=nlog(a)(M)其他性质：性质一：换底公式log(a)(N)=log(b)(N) / log(b)(a)推导如下N = a^[log(a)(N)]a = b^[log(b)(a)]综合两式可得N = {b^[log(b)(a)]}^[log(a)(N)] = b^{[log(a)(N)]*[log(b)(a)]}又因为N=b^[log(b)(N)]所以b^[log(b)(N)] = b^{[log(a)(N)]*[log(b)(a)]}所以log(b)(N) = [log(a)(N)]*[log(b)(a)] {这步不明白或有疑问看上面的}所以log(a)(N)=log(b)(N) / log(b)(a)性质二：（不知道什么名字）log(a^n)(b^m)=m/n*[log(a)(b)]推导如下由换底公式[lnx是log(e)(x),e称作自然对数的底]log(a^n)(b^m)=ln(a^n) / ln(b^n)由基本性质4可得log(a^n)(b^m) = [n*ln(a)] / [m*ln(b)] = (m/n)*{[ln(a)] / [ln(b)]}再由换底公式log(a^n)(b^m)=m/n*[log(a)(b)]--------------------------------------------（性质及推导 完 ）公式三:log(a)(b)=1/log(b)(a)证明如下:由换底公式 log(a)(b)=log(b)(b)/log(b)(a) ----取以b为底的对数,log(b)(b)=1=1/log(b)(a)还可变形得:log(a)(b)*log(b)(a)=1 很高兴为你解答，满意请采纳

log对数函数基本公式是y=logax（a>0 & a≠1）。对数公式是数学中的一种常见公式，如果a^x=N(a>0,且a≠1)，则x叫做以a为底N的对数，记做x=log(a)(N)，其中a要写于log右下。其中a叫做对数的底，N叫做真数。通常我们将以10为底的对数叫做常用对数，以e为底的对数称为自然对数。表达方式（1）常用对数：lg（b）＝log10b（10为底数）。（2）自然对数：ln（b）＝logeb（e为底数）。e为无限不循环小数，通常情况下只取e=2.71828。

对数运算法则，是一种特殊的运算方法。指积、商、幂、方根的对数的运算法则。在数学中，对数是对求幂的逆运算，正如除法是乘法的倒数，反之亦然。这意味着一个数字的对数是必须产生另一个固定数字的指数。一般来说，乘幂允许将任何正实数提高到任何实际功率，总是产生正的结果，因此可以对于b不等于1的任何两个正实数b和x计算对数。由指数和对数的互相转化关系可得出：两个正数的积的对数，等于同一底数的这两个数的对数的和，两个正数商的对数，等于同一底数的被除数的对数减去除数对数的差，一个正数幂的对数，等于幂的底数的对数乘以幂的指数，若式中幂指数则有以下的正数的算术根的对数运算法则：一个正数的算术根的对数，等于被开方数的对数除以根指数。运算法则公式如下：1.lnx+lny=lnxy2.lnx-lny=ln3.lnx_=nlnx4.ln=lnx/n5.lne=16.ln1=0对数的概念：在数学中，对数是对求幂的逆运算，正如除法是乘法的倒数，反之亦然。这意味着一个数字的对数是必须产生另一个固定数字的指数。在简单的情况下，乘数中的对数计数因子。更一般来说，乘幂允许将任何正实数提高到任何实际功率，总是产生正的结果，因此可以对于b不等于1的。

(loga(x))"=1/(xlna)特别地(lnx)"=1/x对数和对数函数是高中数学的重要内容，是高考的必考知识，需要同学们无条件地掌握。但是很多同学在高一时就没有掌握好对数知识，以至于成为整个高中阶段数学学习的绊脚石。大多同学没学好对数知识，主要原因是觉得对数的公式太多，杂乱无章。其中要注意的是：加（减）法则：[f(x)+g(x)]"=f(x)"+g(x)"乘法法则：[f(x)*g(x)]"=f(x)"*g(x)+g(x)"*f(x)除法法则：[f(x)/g(x)]"=[f(x)"*g(x)-g(x)"*f(x)]/g(x)^2log函数对数注意对数起初是为了解决天文学中的计算问题而产生的，因为实际应用性强，所以应用范围更广。特别是，在自然科学中，自然对数lnx应用更加普遍。在高考中，对数问题比比皆是，尤其是函数与导数压轴题中，经常出现自然对数函数f(x)=lnx及复合函数。因而，对数函数是复习函数的重中之重。

1、a^log(a)(b)=b 2、log(a)(a)=1 3、log(a)(MN)=log(a)(M)+log(a)(N); 4、log(a(M÷N) =log(a)(M)-log(a)(N) 5、log(a)(M^n)=nlog(a)(M) 6、log(a)[M^（1/n）]=log(a)(M)/n （注：上文^均为上标符号,例：a^n即为a的n次方）　　7.logab*logba=1

01 log公式运算法则有：loga(MN)=logaM+logaN；loga(M/N)=logaM-logaN；logaNnx=nlogaM。如果a=em，则m为数a的自然对数，即lna=m，e=2.718281828u2026为自然对数的底，其为无限不循环小数。定义：若an=b（a>0，au22601）则n=logab。 自然对数的运算公式和法则：loga(MN)=logaM+logaN；loga(M/N)=logaM－logaN；对logaM中M的n次方有=nlogaM；如果a=e^m，则m为数a的自然对数，即lna=m，e=2.718281828u2026为自然对数的底。 e是“指数”（exponential）的首字母，也是欧拉名字的首字母。和圆周率u03c0及虚数单位i一样，e是最重要的数学常数之一。第一次把e看成常数的是雅各布u2022伯努利，他尝试计算lim（1+1/n） n 的值，1727年欧拉首次用小写字母“e”表示这常数，此后遂成标准。 自然对数的底e是一个令人不可思议的常数，一个由lim(1+1/n)^n定义出的常数，居然在数学和物理中频频出现，简直可以说是无处不在。这实在是让我们不得不敬畏这神奇的数学世界。

logaMN＝logaM+logaN logaM/logaN=logaM-logaN logaM^n=nlogaM logbN=logaNb/logab logaB乘logbA=1 logaB*logbC*logcD=logaD loga(m)b(n)=n/mlogaB 1.换底公式 log(a)(N)=log(b)(N) / log(b)(a) 设N＝logab（表示以a为底b的对数） 2.b＝a^N lnb=Nlna N=lnb/lna

a^y=x→y=log(a)(x) [y=log以a为底x的对数]这就是将指数转换为对数。对数函数的一般形式为 y=logax，它实际上就是指数函数的反函数（图象关于直线y=x对称的两函数互为反函数），可表示为x=a^y，因此指数函数里对于a存在规定——a>0且a≠1，对于不同大小a会形成不同的函数图形：关于X轴对称，当a>1时，a越大，图像越靠近x轴、当0<a<1时，a越小，图像越靠近x轴。a叫做对数的底数，N叫做真数：1、特别地，我们称以10为底的对数叫做常用对数（common logarithm），并记为lgN。2、称以无理数e（e=2.71828…）为底的对数称为自然对数（natural logarithm），并记为lnN。3、零没有对数。4、在实数范围内，负数无对数。在虚数范围内，负数是有对数的。

公式如下：1、a^log(a)(b)=b2、log(a)(a)=13、log(a)(MN)=log(a)(M)+log(a)(N);4、log(a)(M÷N)=log(a)(M)-log(a)(N);5、log(a)(M^n)=nlog(a)(M)6、log(a)[M^（1/n）]=log(a)(M)/n7、logab*logba=18、log(a^n)(b^m)=log(e^y)(e^x)=x/y　　x=ln(b^m),y=ln(a^n)　　得：log(a^n)(b^m)=ln(b^m）÷ln(a^n)希望我的回答能够帮到你。

自然对数是以常数e为底数的对数，记作lnN（N>0）。对数ln公式：ln ( mn ) =ln m +ln n ;ln ( m / n ) =ln m -ln n ;ln （ m ^ n ) =nln m ;ln 1 =0;ln e =1。 自然对数是以常数e为底数的对数，记作lnN(N>0)。在物理学，生物学等自然科学中有重要的意义，一般表示方法为lnx。数学中也常见以logx表示自然对数。常数e的含义是单位时间内，持续的翻倍增长所能达到的极限值。当自然对数lnN中真数为连续自变量时，称为对数函数，记作y=lnx(x为自变量，y为因变量)。 一般地，对数函数是以幂(真数)为自变量，指数为因变量，底数为常量的函数。对数函数是6类基本初等函数之一。其中对数的定义：如果ax=N(a>0，且a≠1)，那么数x叫做以a为底N的对数，记作x=logaN，读作以a为底N的对数，其中a叫做对数的底数，N叫做真数。 一般地，函数y=logaX(a>0，且a≠1)叫做对数函数，也就是说以幂(真数)为自变量，指数为因变量，底数为常量的函数，叫对数函数。其中x是自变量，函数的定义域是(0，+∞)，即x>0。它实际上就是指数函数的反函数，可表示为x=ay。因此指数函数里对于a的规定，同样适用于对数函数。

1)性质：①loga(1)=0；②loga(a)=1；③负数与零无对数.2)运算法则：①loga(MN)=logaM+logaN；②loga(M/N)=logaM－logaN；③对logaM中M的n次方有=nlogaM；如果a=e^m，则m为数a的自然对数，即lna=m，e=2.718281828…为自然对数的底。3)换底公式logaN=(logmN)/(logma)换底公式4)推导公式log(1/a)(1/b)=loga(b)loga(b)*logb(a)=15)求导数(logax)"=1/xlna特殊的即a=e时有(lnx)"=1/x

1对数的概念如果a(a>0,且a≠1)的b次幂等于N,即ab=N,那么数b叫做以a为底N的对数,记作：logaN=b,其中a叫做对数的底数,N叫做真数.由定义知：①负数和零没有对数;②a>0且a≠1,N>0;③loga1=0,logaa=1,alogaN=N,logaab=b.特别地,以10为底的对数叫常用对数,记作log10N,简记为lgN；以无理数e(e=2.71828…)为底的对数叫做自然对数,记作logeN,简记为lnN.2对数式与指数式的互化式子名称abN指数式ab=N(底数)(指数)(幂值)对数式logaN=b(底数)(对数)(真数)3对数的运算性质如果a>0,a≠1,M>0,N>0,那么(1)loga(MN)=logaM+logaN.(2)logaMN=logaM-logaN.(3)logaMn=nlogaM(n∈R).问：①公式中为什么要加条件a>0,a≠1,M>0,N>0?②logaan=?(n∈R)③对数式与指数式的比较.(学生填表)式子ab=NlogaN=b名称a—幂的底数b—N—a—对数的底数b—N—运算性质am·an=am+nam÷an=(am)n=(a>0且a≠1,n∈R)logaMN=logaM+logaNlogaMN=logaMn=(n∈R)(a>0,a≠1,M>0,N>0)难点疑点突破对数定义中,为什么要规定a＞0,且a≠1?理由如下：①若a＜0,则N的某些值不存在,例如log-28ue010②若a=0,则N≠0时b不存在；N=0时b不惟一,可以为任何正数ue010③若a=1时,则N≠1时b不存在；N=1时b也不惟一,可以为任何正数ue010为了避免上述各种情况,所以规定对数式的底是一个不等于1的正数ue010解题方法技巧1(1)将下列指数式写成对数式：①54=625；②2-6=164；③3x=27；④13m=5ue01073.（2）将下列对数式写成指数式：①log1216=-4；②log2128=7；③log327=x；④lg0.01=-2；⑤ln10=2.303；⑥lgπ=k.解析由对数定义：ab=Nue039logaN=b.解答(1)①log5625=4.②log2164=-6.③log327=x.④log135.73=m.解题方法指数式与对数式的互化,必须并且只需紧紧抓住对数的定义：ab=Nue039logaN=b.(2)①12-4=16.②27=128.③3x=27.④10-2=0.01.⑤e2.303=10.⑥10k=π.2根据下列条件分别求x的值：(1)log8x=-23；(2)log2(log5x)=0；(3)logx27=31+log32；(4)logx(2+3)=-1.解析(1)对数式化指数式,得：x=8-23=?(2)log5x=20=1.x=?(3)31+log32=3×3log32=?27=x?(4)2+3=x-1=1x.x=?解答(1)x=8-23=(23)-23=2-2=14.(2)log5x=20=1,x=51=5.(3)logx27=3×3log32=3×2=6,∴x6=27=33=(3)6,故x=3.(4)2+3=x-1=1x,∴x=12+3=2-3.解题技巧①转化的思想是一个重要的数学思想,对数式与指数式有着密切的关系,在解决有关问题时,经常进行着两种形式的相互转化.②熟练应用公式：loga1=0,logaa=1,alogaM=M,logaan=n.3已知logax=4,logay=5,求A=〔x·3x-1y2〕12的值.解析思路一,已知对数式的值,要求指数式的值,可将对数式转化为指数式,再利用指数式的运算求值；思路二,对指数式的两边取同底的对数,再利用对数式的运算求值ue010解答解法一∵logax=4,logay=5,∴x=a4,y=a5,∴A=x512y-13=(a4)512(a5)-13=a53·a-53=a0=1.解法二对所求指数式两边取以a为底的对数得logaA=loga(x512y-13)=512logax-13logay=512×4-13×5=0,∴A=1.解题技巧有时对数运算比指数运算来得方便,因此以指数形式出现的式子,可利用取对数的方法,把指数运算转化为对数运算.4设x,y均为正数,且x·y1+lgx=1(x≠110),求lg(xy)的取值范围.解析一个等式中含两个变量x、y,对每一个确定的正数x由等式都有惟一的正数y与之对应,故y是x的函数,从而lg(xy)也是x的函数.因此求lg(xy)的取值范围实际上是一个求函数值域的问题,怎样才能建立这种函数关系呢?能否对已知的等式两边也取对数?解答∵x>0,y>0,x·y1+lgx=1,两边取对数得：lgx+(1+lgx)lgy=0.即lgy=-lgx1+lgx(x≠110,lgx≠-1).令lgx=t,则lgy=-t1+t(t≠-1).∴lg(xy)=lgx+lgy=t-t1+t=t21+t.解题规律对一个等式两边取对数是解决含有指数式和对数式问题的常用的有效方法；而变量替换可把较复杂问题转化为较简单的问题.设S=t21+t,得关于t的方程t2-St-S=0有实数解.∴Δ=S2+4S≥0,解得S≤-4或S≥0,故lg(xy)的取值范围是(-∞,-4〕∪〔0,+∞).5求值：(1)lg25+lg2·lg50+(lg2)2；(2)2log32-log3329+log38-52log53；(3)设lga+lgb=2lg(a-2b),求log2a-log2b的值;(4)求7lg20·12lg0.7的值.解析(1)25=52,50=5×10.都化成lg2与lg5的关系式.(2)转化为log32的关系式.(3)所求log2a-log2b=log2ab由已知等式给出了a,b之间的关系,能否从中求出ab的值呢?(4)7lg20·12lg0.7是两个指数幂的乘积,且指数含常用对数,设x=7lg20·12lg0.7能否先求出lgx,再求x?解答(1)原式=lg52+lg2·lg(10×5)+(lg2)2=2lg5+lg2·(1+lg5)+(lg2)2=lg5·(2+lg2)+lg2+(lg2)2=lg102·(2+lg2)+lg2+(lg2)2=(1-lg2)(2+lg2)+lg2+(lg2)2=2-lg2-(lg2)2+lg2+(lg2)2=2.(2)原式=2log32-(log325-log332)+log323-5log59=2log32-5log32+2+3log32-9=-7.(3)由已知lgab=lg(a-2b)2(a-2b>0),∴ab=(a-2b)2,即a2-5ab+4b2=0.∴ab=1或ab=4,这里a>0,b>0.若ab=1,则a-2b0,a≠1,c>0,c≠1,N>0)；(2)logab·logbc=logac；(3)logab=1logba(b>0,b≠1)；(4)loganbm=mnlogab.解析(1)设logaN=b得ab=N,两边取以c为底的对数求出b就可能得证.(2)中logbc能否也换成以a为底的对数.(3)应用(1)将logab换成以b为底的对数.(4)应用(1)将loganbm换成以a为底的对数.解答(1)设logaN=b,则ab=N,两边取以c为底的对数得：b·logca=logcN,∴b=logcNlogca.∴logaN=logcNlogca.(2)由(1)logbc=logaclogab.所以logab·logbc=logab·logaclogab=logac.(3)由(1)logab=logbblogba=1logba.解题规律(1)中logaN=logcNlogca叫做对数换底公式,(2)(3)(4)是(1)的推论,它们在对数运算和含对数的等式证明中经常应用.对于对数的换底公式,既要善于正用,也要善于逆用.(4)由(1)loganbm=logabmlogaan=mlogabnlogaa=mnlogab.7已知log67=a,3b=4,求log127.解析依题意a,b是常数,求log127就是要用a,b表示log127,又3b=4即log34=b,能否将log127转化为以6为底的对数,进而转化为以3为底呢?解答已知log67=a,log34=b,∴log127=log67log612=a1+log62.又log62=log32log36=log321+log32,由log34=b,得2log32=b.∴log32=b2,∴log62=b21+b2=b2+b.∴log127=a1+b2+b=a(2+b)2+2b.解题技巧利用已知条件求对数的值,一般运用换底公式和对数运算法则,把对数用已知条件表示出来,这是常用的方法技巧ue0108已知x,y,z∈R+,且3x=4y=6z.(1)求满足2x=py的p值；(2)求与p最接近的整数值；(3)求证：12y=1z-1x.解析已知条件中给出了指数幂的连等式,能否引进中间量m,再用m分别表示x,y,z?又想,对于指数式能否用对数的方法去解答?解答（1）解法一3x=4yue03clog33x=log34yue03cx=ylog34ue03c2x=2ylog34=ylog316,∴p=log316.解法二设3x=4y=m,取对数得：x·lg3=lgm,ylg4=lgm,∴x=lgmlg3,y=lgmlg4,2x=2lgmlg3,py=plgmlg4.由2y=py,得2lgmlg3=plgmlg4,∴p=2lg4lg3=lg42lg3=log316.(2)∵2=log390,a2+b2=7ab.求证式中真数都只含a,b的一次式,想：能否将真数中的一次式也转化为二次,进而应用a2+b2=7ab?解答logma+b3=logm(a+b3)212=解题技巧①将a+b3向二次转化以利于应用a2+b2=7ab是技巧之一.②应用a2+b2=7ab将真数的和式转化为ab的乘积式,以便于应用对数运算性质是技巧之二.12logma+b32=12logma2+b2+2ab9.∵a2+b2=7ab,∴logma+b3=12logm7ab+2ab9=12logmab=12(logma+logmb),即logma+b3=12(logma+logmb).思维拓展发散1数学兴趣小组专门研究了科学记数法与常用对数间的关系.设真数N=a×10n.其中N>0,1≤alogk44>logk66>0,∴3x0).∴10t>1,ax2-2(a+1)x-1>1,∴ax2-2(a+1)x-2>0.①当a=0时,解集｛x|x

对数函数的公式是：（1）log(a)(MN)=log(a)(M)+log(a)(N)。（2）log(a)(M/N)=log(a)(M)-log(a)(N)。（3）log(a)(M^n)=nlog(a)(M) （n∈R）。（4）log(a^n)(M)=1/nlog(a)(M)(n∈R)。（5）换底公式：log(A)M=log(b)M/log(b)A (b>0且b≠1）。（6）log(a^n)M^m=(m/n)log(a)M。（7）对数恒等式：a^log（a)N=N; 　log（a）a^b=b。对数公式是数学中的一种常见公式，如果a^x=N(a>0,且a≠1)，则x叫做以a为底N的对数，记做x=log(a)(N)，其中a要写于log右下。其中a叫做对数的底，N叫做真数。通常我们将以10为底的对数叫做常用对数，以e为底的对数称为自然对数。

对数函数的公式是x=log(a)(N)。对数公式是数学中的一种常见公式，如果a^x=N(a>0，且a≠1)，则x叫做以a为底N的对数，记做x=log(a)(N)，其中a要写于log右下。其中a叫做对数的底，N叫做真数。通常我们将以10为底的对数叫做常用对数，以e为底的对数称为自然对数。实际应用：通常我们将以10为底的对数叫常用对数（common logarithm），并把log10N记为lgN。另外，在科学计数中常使用以无理数e=2.71828，为底数的对数，以e为底的对数称为自然对数（natural logarithm），并且把logeN记为In N。

加法公式：同一底数的这两个数的对数的和等于两个正数的积的对数；减法公式：同一底数的被除数的对数减去除数对数的差等于两个正数商的对数。扩展资料：1、一个正数幂的对数，等于幂的底数的对数乘以幂的指数，即2、若式中幂指数则有以下的正数的算术根的对数运算法则:一个正数的算术根的对数，等于被开方数的对数除以根指数，即参考资料来源：百度百科-对数运算法则

对数函数计算公式如下：1、a^(log(a)(b))=b。2、log(a)(a^b)=b。3、log(a)(MN)=log(a)(M)+log(a)(N)。4、log(a)(M÷N)=log(a)(M)-log(a)(N)。5、log(a)(M^n)=nlog(a)(M)。6、log(a^n)M=1/nlog(a)(M)。对数相关应用：对数在数学内外有许多应用。这些事件中的一些与尺度不变性的概念有关。例如，鹦鹉螺的壳的每个室是下一个的大致副本，由常数因子缩放。这引起了对数螺旋。Benford关于领先数字分配的定律也可以通过尺度不变性来解释。对数也与自相似性相关。例如，对数算法出现在算法分析中，通过将算法分解为两个类似的较小问题并修补其解决方案来解决问题。自相似几何形状的尺寸，即其部分类似于整体图像的形状也基于对数。对数刻度对于量化与其绝对差异相反的值的相对变化是有用的。此外，由于对数函数log(x)对于大的x而言增长非常缓慢，所以使用对数标度来压缩大规模科学数据。对数也出现在许多科学公式中，例如Tsiolkovsky火箭方程，Fenske方程或能斯特方程。

对数函数没有特定的积分公式，一般按照分部积分来计算。例如：积分ln(x)dx原式=xlnx-∫xdlnx=xlnx-∫x*1/xdx=xlnx-∫dx=xlnx-x+c1.一般地，如果ax=n（a>0，且a≠1），那么数x叫做以a为底n的对数，记作x=logan，读作以a为底n的对数，其中a叫做对数的底数，n叫做真数。2.一般地，函数y=logax（a>0，且a≠1）叫做对数函数，也就是说以幂为自变量，指数为因变量，底数为常量的函数，叫对数函数。3.积分是微分的逆运算，即知道了函数的导函数，反求原函数。在应用上，积分作用不仅如此，它被大量应用于求和，通俗的说是求曲边三角形的面积，这巧妙的求解方法是积分特殊的性质决定的。

在对数函数中，当a>0且a≠1时,M>0,N>0,那么：logu2090(MN)=logu2090M+logu2090N；logu2090(M/N)=logu2090M-logu2090N；logu2090(M^n)=nlogu2090M（n∈R） 。

对数公式推导：log(1/a)(1/b)=log(a^-1)(b^-1)=-1logab/-1=loga(b)，loga(b)×logb(a)=1，loge(x)=ln(x)，lg(x)=log10(x)。对数公式是数学中的一种常见公式，如果a^x=N(a>0，且a≠1)，则x叫做以a为底N的对数，记做x=log(a)(N)，其中a要写于log右下。其中a叫做对数的底，N叫做真数。通常将以10为底的对数叫做常用对数，以e为底的对数称为自然对数。

log公式运算公式：loga(MN)=logaM+logaN;loga(M/N)=logaM-logaN； logaNnx=nlogaM。log梗概：对数（logarithm）是对求幂的逆运算，一个数字的对数是必须产生另一个固定数字（基数）的指数。对数的符号log出自拉丁文logarithm，最早由意大利数学家卡瓦列里（Cavalieri）所使用。如果a的x次方等于N(a>0，且a不等于1)，那么数x叫做以a为底N的对数，记作x=logaN。其中，a叫做对数的底数，N叫做真数。对数在数学内外有许多应用。这些事件中的一些与尺度不变性的概念有关。例如，鹦鹉螺的壳的每个室是下一个的大致副本，由常数因子缩放。这引起了对数螺旋。Benford关于领先数字分配的定律也可以通过尺度不变性来解释。对数也与自相似性相关。例如，对数算法出现在算法分析中，通过将算法分解为两个类似的较小问题并修补其解决方案来解决问题。自相似几何形状的尺寸，即其部分类似于整体图像的形状也基于对数。对数刻度对于量化与其绝对差异相反的值的相对变化是有用的。此外，由于对数函数log（x）对于大的x而言增长非常缓慢，所以使用对数标度来压缩大规模科学数据。对数也出现在许多科学公式中，例如Tsiolkovsky火箭方程，Fenske方程或能斯特方程。

用^表示乘方，用log(a)(b)表示以a为底，b的对数*表示乘号，/表示除号定义式：若a^n=b(a>0且a≠1)则n=log(a)(b)基本性质：1.a^(log(a)(b))=b2.log(a)(MN)=log(a)(M)+log(a)(N);3.log(a)(M/N)=log(a)(M)-log(a)(N);4.log(a)(M^n)=nlog(a)(M)推导1.这个就不用推了吧，直接由定义式可得(把定义式中的[n=log(a)(b)]带入a^n=b)2.MN=M*N由基本性质1(换掉M和N)a^[log(a)(MN)]=a^[log(a)(M)]*a^[log(a)(N)]由指数的性质a^[log(a)(MN)]=a^{[log(a)(M)]+[log(a)(N)]}又因为指数函数是单调函数，所以log(a)(MN)=log(a)(M)+log(a)(N)3.与2类似处理MN=M/N由基本性质1(换掉M和N)a^[log(a)(M/N)]=a^[log(a)(M)]/a^[log(a)(N)]由指数的性质a^[log(a)(M/N)]=a^{[log(a)(M)]-[log(a)(N)]}又因为指数函数是单调函数，所以log(a)(M/N)=log(a)(M)-log(a)(N)4.与2类似处理M^n=M^n由基本性质1(换掉M)a^[log(a)(M^n)]={a^[log(a)(M)]}^n由指数的性质a^[log(a)(M^n)]=a^{[log(a)(M)]*n}又因为指数函数是单调函数，所以log(a)(M^n)=nlog(a)(M)

对数运算10个公式如下：1、lnx+lny=lnxy。2、lnx-lny=ln(x/y)。3、Inxn=nlnx。4、In(n√x)=lnx/n。5、lne=1。6、In1=0。7、Iog(A*B*C)=logA+logB+logC；logA"n=nlogA。8、logaY =logbY/logbA。9、log(a)(MN)=log(a)(M)+log(a)(N)。10、Iog(A)M=log(b)M/log(b)A(b>0Eb#1)。对数介绍在数学中，对数是对求幂的逆运算，正如除法是乘法的倒数，反之亦然。这意味着一个数字的对数是必须产生另一个固定数字（基数）的指数。在简单的情况下，乘数中的对数计数因子。更一般来说，乘幂允许将任何正实数提高到任何实际功率，总是产生正的结果，因此可以对于b不等于1的任何两个正实数b和x计算对数。

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定义： 　　若a^n=b(a>0且a≠1) 　　则n=log(a)(b) 　　基本性质： 　　1、a^(log(a)(b))=b 　　2、log(a)(MN)=log(a)(M)+log(a)(N); 　　3、log(a)(M÷N)=log(a)(M)-log(a)(N); 　　4、log(a)(M^n)=nlog(a)(M) 　　推导 　　1、因为n=log(a)(b)，代入则a^n=b，即a^(log(a)(b))=b。 　　2、MN=M×N 　　由基本性质1(换掉M和N) 　　a^[log(a)(MN)] = a^[log(a)(M)]×a^[log(a)(N)] 　　由指数的性质 　　a^[log(a)(MN)] = a^{[log(a)(M)] + [log(a)(N)]} 　　又因为指数函数是单调函数，所以 　　log(a)(MN) = log(a)(M) + log(a)(N) 　　3、与（2）类似处理 　　MN=M÷N 　　由基本性质1(换掉M和N) 　　a^[log(a)(M÷N)] = a^[log(a)(M)]÷a^[log(a)(N)] 　　由指数的性质 　　a^[log(a)(M÷N)] = a^{[log(a)(M)] - [log(a)(N)]} 　　又因为指数函数是单调函数，所以 　　log(a)(M÷N) = log(a)(M) - log(a)(N) 　　4、与（2）类似处理 　　M^n=M^n 　　由基本性质1(换掉M) 　　a^[log(a)(M^n)] = {a^[log(a)(M)]}^n 　　由指数的性质 　　a^[log(a)(M^n)] = a^{[log(a)(M)]*n} 　　又因为指数函数是单调函数，所以 　　log(a)(M^n)=nlog(a)(M)　　基本性质4推广　　log(a^n)(b^m)=m/n*[log(a)(b)]　　推导如下：　　由换底公式（换底公式见下面）[lnx是log(e)(x)，e称作自然对数的底] 　　log(a^n)(b^m)=ln(b^m)÷ln(a^n)　　由基本性质4可得　　log(a^n)(b^m) = [m×ln(b)]÷[n×ln(a)] = (m÷n)×{[ln(b)]÷[ln(a)]}　　再由换底公式　　log(a^n)(b^m)=m÷n×[log(a)(b)] --------------------------------------------（性质及推导 完） 编辑本段函数图象　　1.对数函数的图象都过(1,0)点.　　2.对于y=log(a)(n)函数, 　　①,当0<a<1时,图象上函数显示为(0,+∞)单减.随着a 的增大,图象逐渐以(1,0)点为轴顺时针转动,但不超过X=1.　　②当a>1时,图象上显示函数为(0,+∞)单增,随着a的增大,图象逐渐以(1.0)点为轴逆时针转动,但不超过X=1.　　3.与其他函数与反函数之间图象关系相同,对数函数和指数函数的图象关于直线y=x对称. 编辑本段其他性质　　性质一：换底公式　　log(a)(N)=log(b)(N)÷log(b)(a)　　推导如下：　　N = a^[log(a)(N)]　　a = b^[log(b)(a)]　　综合两式可得　　N = {b^[log(b)(a)]}^[log(a)(N)] = b^{[log(a)(N)]*[log(b)(a)]}　　又因为N=b^[log(b)(N)]　　所以 b^[log(b)(N)] = b^{[log(a)(N)]*[log(b)(a)]}　　所以 log(b)(N) = [log(a)(N)]*[log(b)(a)] {这步不明白或有疑问看上面的}　　所以log(a)(N)=log(b)(N) / log(b)(a)　　公式二：log(a)(b)=1/log(b)(a)　　证明如下：　　由换底公式 log(a)(b)=log(b)(b)/log(b)(a) ----取以b为底的对数　　log(b)(b)=1 =1/log(b)(a) 还可变形得: log(a)(b)×log(b)(a)=1 　　在实用上，常采用以10为底的对数，并将对数记号简写为lgb,称为常用对数，它适用于求十进伯制整数或小数的对数。例如lg10=1,lg100=lg102=2,lg4000=lg（103×4）=3+lg4,可见只要对某一范围的数编制出对数表，便可利用来计算其他十进制数的对数的近似值。在数学理论上一般都用以无理数e=2.7182818……为底的对数，并将记号 loge。简写为ln，称为自然对数，因为自然对数函数的导数表达式特别简洁，所以显出了它比其他对数在理论上的优越性。历史上，数学工作者们编制了多种不同精确度的常用对数表和自然对数表。但随着电子技术的发展，这些数表已逐渐被现代的电子计算工具所取代。

加法公式：同一底数的这两个数的对数的和等于两个正数的积的对数；减法公式：同一底数的被除数的对数减去除数对数的差等于两个正数商的对数。扩展资料：1、一个正数幂的对数，等于幂的底数的对数乘以幂的指数，即2、若式中幂指数则有以下的正数的算术根的对数运算法则:一个正数的算术根的对数，等于被开方数的对数除以根指数，即参考资料来源：百度百科-对数运算法则

log(a^n)(M)=log(a)(M)/log(a)(a^n)=log(a)(M)/n.也就是说x等于n分之一。其中第一个等号是用换底公式算的，换底公式是log(a)(b)=log(c)(b)/log(c)(a).

lg对数的计算公式：a^(log(a)(N))=a^t。对数公式是数学中的一种常见公式，如果a^x=N(a>0，且a≠1)，则x叫做以a为底N的对数，记做x=log(a)(N)，其中a要写于log右下。其中a叫做对数的底，N叫做真数。通常我们将以10为底的对数叫做常用对数，以e为底的对数称为自然对数。一个数，它的对数是已知数，就称此数为已知数的真数。真数亦称反对数，是相对于假数(即对数)而言的数。始见于《数理精蕴》下编卷三十八“对数比例”。设a是个不等于1的正数，即a>0，且a≠1。若ap=b，则称p为b的以a为底的对数；而称b为p的以a为底的真数。记作p=logab。例如，以2为底，则8的对数是3，3的真数是8。

举个例子 loga b=lgb/lga 证明令loga b=x则a^x=b两边取10的对数lga^x=lgbxlga=lgbx=lgb/lga因为loga b=x∴loga b=lgb/lga

综述：lnx+ lny=lnxy。对数运算法则(rule of logarithmic operations）是对数函数一般运算法则，包括积、商、幂、方根等的运算。由指数和对数的互相转化关系可得出:两个正数的积的对数，等于同一底数的这两个数的对数的和。参考资料来源：百度百科－对数运算法则

1、lnx+lny=lnxy；2、lnx-lny=ln(x/y)；3、Inxn=nlnx；4、In(n√x)=lnx/n；5、lne=1；6、In1=0；7、Iog(A*B*C)=logA+logB+logC；logA"n=nlogA；8、logaY =logbY/logbA；9、log(a)(MN)=log(a)(M)+log(a)(N)；10、Iog(A)M=log(b)M/log(b)A(b>0Eb#1)。推导公式：1、log(1/a)(1/b)=log(a^-1)(b^-1)=-1logab/-1=loga(b)；2、loga(b)*logb(a)=1；3、loge(x)=ln(x)；4、lg(x)=log10(x)。

运算法则公式如下：1、lnx＋ lny＝lnxy2、lnx－lny＝ln（x／y）3、lnxu207f＝nlnx4、ln（u207f√dux）＝lnx／n5、lne＝16、ln1＝0相关简介1、对数公式是数学中的一种常见公式，如果a^x=N(a>0,且a≠1)，则x叫做以a为底N的对数，记做x=log(a)(N)，其中a要写于log右下。其中a叫做对数的底，N叫做真数。通常我们将以10为底的对数叫做常用对数，以e为底的对数称为自然对数。2、对数运算，实际上也就是指数在运算。

英语作文要想写得好，离不开平时的积累，高分作文一般胜在行文清晰、准确、简洁三点，这就是公认的英语满分作文“黄金三定律”，为保证所写文章清晰明了，一是越确切具体越好，二是组织结构富有逻辑性。姐姐现在就为你们提供三篇与英语作文题目有关的范文，记得好好参考哦，如果对你有帮助记得点个赞再走。【一】U0001f338U0001f338U0001f338案例来咯英语作文：Recently, more and more universities have realized the importance of creating a green campus. It has become a new trend throughout the country.So what do we mean by green campus? On the one hand, the protection of the environment is necessary, and there is no denying that this is the premise of this concept. On the other hand, it is far from enough to keep the green environment simple in order to meet the overall goal of the green campus. On the contrary, it needs all the staff and all our efforts, the positive cultural atmosphere of the students.Therefore, in order to create green campus, first, it is necessary, everyone thinks of our own host campus, and to realize green enlightenment brings us a house. More importantly, action is needed to achieve that goal. Last but not least, we can spread the spirit, the broader area, and call for more people to join the project.翻译：近年来，越来越多的大学意识到创建绿色校园的重要性。这已成为全国各地的一种新趋势。那么，我们所说的绿色校园是什么意思呢？一方面，保护环境是必要的，而且不可否认，这是这一概念的前提。另一方面，它也很遥远 m足以保持绿色环境的简单性，以达到绿色校园的整体目标。相反，它需要所有的员工和我们所有的努力，需要积极的文化氛围 e学生。因此，为了创造绿色校园，首先有必要大家都想到自己的主办校园，实现绿色启蒙给我们带来一所房子。更重要的是，需要采取行动 实现这个目标。最后但并非最不重要的是，我们可以传播精神，更广泛的领域，并呼吁更多的人加入这个项目。【二】U0001f338U0001f338U0001f338案例来咯英语作文：Nowadays,campus construction has been brought into focus. According to a survey,almost all the schools and colleges are rebuilding their campus: not only the teaching buildings but also the circumstances. In this essay,I will discuss the importance of campus construction and offer my own view on it.A lot of efforts have been made to better the campus environment,in particular,the construction of a green campus. Many colleges have taken serious measures to build environmental friendly campus,such as lawns,artificial pools,and tree-lined roads. However,in my view,this is only the initial step and we can do more. To begin with,the schools and colleges may implement strict regulation of waste on campus: no matter the leftovers in canteens or the litter in classrooms. Moreover,on the student side,we can use green bags instead of disposable plastic bags and use more recycling chopsticks and bowls.In addition,the most important thing for everyone is that we should raise our awareness of environmental protection.翻译：如今，校园建设已成为人们关注的焦点。根据一项调查，几乎所有的学校和大学都在重建他们的校园：不仅是教学楼，还有周边建筑 nces.在本文中，我将讨论校园建设的重要性，并提出我自己的看法。为了改善校园环境，特别是绿色校园的建设，人们更加努力。许多高校已采取认真措施建设环保校园 这里有草坪、人工游泳池和绿树成荫的道路。然而，在我看来，这只是第一步，我们可以做得更多。首先，学校和大学可能会对废物o实施严格的管理 n校园：无论是食堂里的剩饭，还是教室里的垃圾。此外，在学生方面，我们可以使用绿色塑料袋代替一次性塑料袋，并使用更多的回收筷子和b 猫头鹰此外，对每个人来说，最重要的事情是，我们应该提高我们的环保意识。【三】U0001f338U0001f338U0001f338案例来咯英语作文：The university school is like another home for our students. Its environment will affect our healthy growth and study. So it is important to create a green campus.The definition of the green campus is not only referred to its green environment, but also its hardworking atmosphere. We must bear these in mind and put these into practice.As the managers of school, they can provide us with beautiful environment. But that is not enough. The campaign to create a green campus needs the participation of every one. Firstly, we should protect the trees, grasslands and flowers in our mother school. Secondly, when we see the behavior of destruction, don"t stand by and do something to combat it. Besides, we also can give wide publicity to creating a green campus.翻译：学校就像我们学生的另一个家。它的环境将影响我们的健康成长和学习。所以创建一个绿色的校园是很重要的。绿色校园的定义不仅是指它的绿色环境，也是指它的勤劳的氛围。我们必须牢记这些问题，并把它们付诸实践。作为学校的管理者，他们可以为我们提供美丽的环境。但这还不够。创建一个绿色校园的运动需要每个人的参与。首先，我们应该提出 在我们母亲的学校里的树木、草原和鲜花。其次，当我们看到破坏的行为时，不要袖手旁观，做些什么来对抗它。此外，我们还可以给予广泛的宣传 创建一个绿色校园。

1、迢迢万里的银河朝西南方向下坠，喔喔的鸡叫之声在邻家不断长鸣。疾病折磨我几乎把救亡壮志消尽，出门四望不禁手搔白发抱憾平生。2、三万里长的黄河奔腾向东流入大海，五千仞高的华山耸入云霄上摩青天。中原人民在胡人压迫下眼泪已流尽，他们盼望王师北伐盼了一年又一年。

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三万里长的黄河奔腾向东流入大海，五千仞高的华山耸入云霄触青天。中原人民在胡人压迫下，眼泪已流尽，他们盼望南宋朝廷军队一年又一年。

1.建设绿色校园十分重要 2.绿色校园不仅指绿色环境 3.为了建设绿色校园我们应该…… 范文一： Nowadays tens of thousands of people are claiming that we should build a green country.As a college student,I think to create a green campus also has great significance. To create a green campus,obviously we have to commit ourselves to protect the environment of our campus first,which is of prime importance.Moreover,in my opinion,green campus not only means the green environment,but also means to create a sustainable developing campus. To create a sustainable developing campus,each university student should have the sense of being masters,which means they should apply themselves to not only improve themselves from all kinds of aspects,but also help universities to improve management,help teachers to improve the quality of teaching,and help schoolmates to improve college life.As long as every college student can do like that,university life will be their great memory in life. 范文二： “Green campus” is,to some extent,a relatively new concept to us.It not only means creating a green environment on campus,but also refers to that the students should be educated and have an environmental sense in their mind.Of course,this concept is very important for the students because it sets goals toward the future of the world. The young generation is under the burden of severe environmental problems and the hopes of environmental improvement are lying in them.Therefore,campus plays a more important role in educating the young generation.The creation of “Green campus” will greatly stimulate students to take part in various environmental protection activities; most importantly,students will be educated to take environmental problems seriously as their own mission and responsibility.Under such stimulations,students may grasp the chance to learn every necessary course for the harmonious and sustainable development of the world. To bring “green campus” to its full play,effective measures should be taken.First,based on its education function,campus should bring the theory of “sustainable development” into classrooms,set environmental management rules and conduct environmental education activities.Second,campus also needs to strengthen its ties with the society,tries to communicate with parents and experts so as to ensure that students could have a better participation in the practical activities.Only by the co-efforts of the whole society could “green campus” work smoothly and bring benefit to people"s well-beings.

6月：Part I WritingFree Admission to Museums（满分版）Nowadays, an increasing number of museums are admission-free to visitors home and abroad. The hidden reason behind this is not hard to analyze as there"s a growing awareness for the authorities regarding the urgency of popularization of culture, knowledge and history with every average person in our society. Only with free access to this live ‘database", can most people fully enjoy what museums could offer to them.However, free admission to museums might lead to some social problems as well. The most obvious problem is that it might give museums a very heavy economic burden which directly impedes the sustainable development of these organizations. As a result, our government has to work out other ways to collect funds from different channels, which might be difficult to operate or control. On the other hand, free admission attracts too many visitors, some of which might not be well-purposed and do some conscious or unconscious damage to the valuable treasures which used to be well-preserved in the museums. As a university student, I am in favor of the free-admission conduct. Yet it is proposed that some measures should be taken to solve the potential problems caused by it. For example, museums can make some regulations to guide the behavior of visitors or set some ‘closed" days for museums for regular maintenance. Only in this way can free-admission to museums become a long-lasting phenomenon and have sustainable development.Part II Reading Comprehension (Skimming and Scanning)阅读答案　　1. A. He just wouldn"t look her in the dye。　　2. C cultural ignorance　　3.B Increasing understanding of people of other cultures。　　4.B A personnel training company。　　5. D he must get rid of his gender bias　　6.C It helped him make fair decisions。　　7.A He told him to get the dates right。　　8. embarrassed　　9. inclusiveness　　10. differences and similarities　　听力：　　短对话　　11. She has always enjoyed great popularity　　12. They are going to have a holiday　　13. He was very courageous　　14. Buy a new washing machine　　15. He is not excited about his new position　　16. The man offers to drive the women to the party　　17. Finalizing a contract　　18. She ordered some paper　　长对话　　19 He can no longer work at sea　　20 She passed away years ago　　21 She has never got on with her father　　22 He is excellent but looks bad-tempered　　23 Some of the packs do not contain manuals　　24 solve the problem at her company"s cost　　25 Ideal　　短文：　　26 C it"s entertaining　　27C they may catch some disease　　28D continue the feeding till it get warm　　29C he will lie whenever he wants　　30A she made him apologize　　31D move furniture for her　　32A the atmosphere they live in is rather unreal　　33D he has too much to know the value of things　　34D she has no time to do it herself　　35D the lifestyle depicted in Hollywood movies　　复合式听写答案： 　　36 concentrated 40 row 　　37 information 41 suspected　　38 depends 42 phenomenon (现象)　　39 straight 43 efficiently　　44 our second rule of learning is this: it is better to study fairly briefly but often。　　45 Let"s say you are trying to learn some new and rather difficult English vocabulary using a stack of cards。　　46 The answer is it is better to space out the presentations of the word you are to learn。　　47. M require 48. I painful 49.F especially 50. E enormous 51.H mission 52. D enhance 53. B daily 54.J performance 55. K profession 56 A daily　　57 A it inspired many leading designers to start going green　　58 D quality organic replacements for synthetics are not readily available 　　59 D are gaining more and more support　　60 A she doesn"t seem to care about it　　61 B it has a very promising future　　62 B a person"s hair may reveal where they have lived。　　63 C food and drink leave traces in one"s body tissues　　64 B the water it delivers becomes lighter when it moves inland。　　65 D a chart illustrating the movement of the rain system。　　66 C it helps the police narrow down possibililities in detective work。　　完型：67. D. budget 68. A. mostly 69. B. besides 70. D. trend 71.D. particularly 72. A. while 73. D. shaking 74. B. if 75. D. larger 76.D. in view of 77. A. unique 78. A. over 79. D. decay 80. A. proceeded 81.B. widening 82. B. massive 83. C. vehicles 84. A. or 85. B. predict 86.B. likely 翻译　　87. difficulty (in) catching up with his classmates　　88. wouldn"t have been caught by the rain　　89. more likely to put on weight　　90. What many people don"t realize　　91. closely relative to the lack of exercise12月：范文　　In recent years, extravagance and waste have become increasingly serious in some of the university campus. We can see that papers, bottles and cans are thrown away after use; food is wasted just because of its poor taste; clothes are discarded simply owing to their old fashion. As a consequence, people in mounting numbers put great emphasis on creating a green campus。　　There are at least two criteria to distinguish what is green campus. On the one hand, natural resources must be conserved and made full use of, for example, we, as college students, should take the wise use of papers and second-hand textbooks into account. On the other hand, education to build up thrift habits must be promoted by relevant departments and professionals at various levels。　　Accordingly, it is necessary for us to take effective steps. For one thing, university authorities should respond with the demand for more rigid conservation of our natural resources, such as water, electricity, and so on. For another, we should enhance the awareness of college students that creating a green campus is of utmost significance to both our society and ourselves。　　快速阅读　　1.B revising their financial aid polices　　2.D It cut its merit-based aid to help the needy students　　3.C attract good students　　4. D it"s not right to give aid to those who can afford the tuition　　5. B fierce competition among institutions　　6. B They regard it as a necessary evil　　7. C Many students from middle-income families have come to rely on it　　8. qualified　　9. recognizes　　10. excellence　　听力小对话答案　　11.A, get some small change　　12.B, buying a gift for a child　　13.A, taking photographs　　14.B, he can provide little used information　　15.D, he knows his own imitations　　16.C, her gym exercise has yielded good results。　　17.D, The professor"s suggestion is constructive　　18.A，Indifferent。　　19.C ，he has to work during the day　　20.B，learn data processing　　21.C, every Monday, lasting for 12 weeks　　22.A, what to bring for registration。　　23.D. A financial trader　　24.B, He considers cooking creative　　25. D, It can be a good thing　　短文听力　　26. C Live is not possible in outer space。　　27. C It has a large ocean under its surface。　　28. A LIght is not an essential miles long　　29.B What Dr.Meyer"s instructions exacty were。　　30.D She asks them to repeat what they are supposed to do。　　31.A it lacks the stability of the printed word。　　32.C Challenging work　　33.A Many tedious jobs continue to be done manually。　　34.D Give them responsibilities as part of team。　　35.B They concern a small number of the people only。　　听力复合式听写答案 (36) classified (37) background (38) album (39 )appreciation (40) context (41) implies (42) image (43)instruments (44) Descriptive (45).It tells the reader how to do something, for example, explaining the technique used to shoot a film. (46)Authors may actually use more than one type of technique in the given piece of informational writing.选词填空　　47-51.　　K recruited　　J recording　　L total C aspects　　B analyzed　　52-56.　　H quality　　N unsure　　G established　　A already　　E contributing　　仔细阅读　　passage one　　57. C She will present to the world a new image of African-American women　　58. B They are of an inferior social group　　59. D What Michelle should do as wife and mother in the White House　　60. C However hard she tries, she can"t expect to please everybody　　61. A Help change the prevailing view about black women　　passage two　　62. A Institution worldwide are hiring administrators from the U.S。　　63. B Their ability to raise funds　　64. D Most of their revenues come from the government　　65. A she was known to be good at raising money　　66. C They will view a lot of things from a new perspective　　完型填空　　67.B focuses　　68.D adequate　　69.A currently　　70.C challenges　　71.B retirement　　72.A over　　73.B learning　　74.D on　　75.C needs　　76.D portion　　77.A when　　78.C homes　　79.B ever　　80.A for example　　81.C adjust　　82.D to　　83.B unpredictably　　84.C available　　85.A sense　　86.D roles　　翻译　　87. You would not have failed if___(按照我的指令去做)　　You had followed my orders。　　88. Despite the hardship he encountered, Mark never ___(放弃对知识的追求)　　abandoned the pursuit of knowledge。　　89. Scientists agree that it will be a long time before____(我们找到治愈癌症的方法)　　We find the cure for cancer。　　90. Production has to be increased considerably to ___ . (与消费者不断增长的需求保持同步)　　Keep up with the constantly growing needs of consumers。　　91. The more exercise you take, ____ 。(你越不大可能感冒)　　The less likely you are to catch a cold。

　古诗《秋夜将晓出篱门迎凉有感二首》是宋代诗人陆游的组诗作品。第一首落笔写银河西坠，鸡鸣欲曙，渲染出一种苍茫静寂的气氛，表现了有心杀敌无力回天的感慨。第二首写大好河山，陷于敌手，以“望”字为眼，表现了诗人希望、失望而终不绝望的千回百转的心情。诗境雄伟、严肃、苍凉、悲愤。这是陆游的爱国诗篇。诗文如下：秋夜将晓出篱门迎凉有感 二首 其一迢迢天汉西南落，喔喔邻鸡一再鸣。壮志病来消欲尽，出门搔首怆平生。其二三万里河东入海，五千仞岳上摩天。遗民泪尽胡尘里，南望王师又一年。诗意：其一迢迢万里的银河朝西南方向下坠，喔喔的鸡叫之声在邻家不断长鸣。疾病折磨我几乎把救亡壮志消尽，出门四望不禁手搔白发抱憾平生。其二三万里黄河东流入大海，五千仞华山高耸接青天。铁蹄下遗民欲哭已无泪，盼望官军收失地又一年。这首诗表达了作者爱国和忧国忧民的思想感情。陆游是宋代爱国诗人、词人。他具有多方面文学才能，尤以诗的成就为最，在生前即有“小李白”之称，不仅成为南宋一代诗坛领袖，而且在中国文学史上享有崇高地位。有《剑南诗稿》《渭南文集》《南唐书》《老学庵笔记》《放翁词》《渭南词》等数十个文集传世。

English Composition 2010-12 How Should Parents Help Children to Be Independent? There is no denying the fact that independence plays an increasingly important part in our daily life and we canu2019t help asking such a question: how should parents help children to be independent. To begin with, it is imperative that parents provide opportunities to children and allow them to participate in the social games which contribute to the independence of the children. Whatu2019s more, under the excessive care and protection of parents, these children are lack of the ability to overcome the difficulties that abound in their real life. Therefore, it is a must for parents to cultivate the independence which helps their children easily conquer frustration and depression, To conclude, itu2019s essential for us to dispose of the problem of childrenu2019s independence timely and effectively. Parents should help children develop strong independence and the abilities needed in the future. Only in this way can they be ready to confront any challenges in the society of fierce competition. 2010-06 Due Attention Should Be Given to Spelling Nowadays fewer and fewer students pay attention to their word-spelling. According to a recent survey, there is a dramatic increase in the number of students who can only imitate the pronunciation of a word but be incapable of spelling it. In this essay I will discuss the factors of this phenomenon and offer my own view on it. There are a number of factors that can be accountable for this situation. One of the most common factors is that fewer and fewer students need to write English essays. Besides, the goal of most students to learn English is to speak it and pass the examination which means they just need to select the similar words according to the listening materials and passages. Perhaps the most contributing factor is the wide use of electronic devices such as e-dictionaries and computers and students no longer need to correct the words by themselves. As far as Iu2019m concerned, I firmly argue that we need to attach great importance to word-spelling. To the students, they should write English as much as they can. Meanwhile, to the teachers, the dictations should be reinforced in the class. 2009-12 Create a Green Campus In recent years, extravagance and waste have become increasingly serious in some of the university campus. We can see that papers, bottles and cans are thrown away after use; food is wasted just because of its poor taste; clothes are discarded simply owning to their old fashion. As a consequence, people in mounting numbers put great emphasis on creating a green campus. There are at least two criteria to distinguish what is green campus. On the one hand, natural resources must be conserved and made full use of, for example, we, as college students, should take the wise use of papers and second-hand textbook into account. On the other hand, education to build up thrift habits must be prompt by relevant departments and professionals at various levels. Accordingly, it is necessary for us to take effective steps. For one thing, university authorities should respond with the demand for more natural resources, such as water, electricity, and so on. For another, we should enhance the awareness of college students that creating a green campus is of utmost significance to both our society and ourselves. English Composition 2010-12 How Should Parents Help Children to Be Independent? There is no denying the fact that independence plays an increasingly important part in our daily life and we canu2019t help asking such a question: how should parents help children to be independent. To begin with, it is imperative that parents provide opportunities to children and allow them to participate in the social games which contribute to the independence of the children. Whatu2019s more, under the excessive care and protection of parents, these children are lack of the ability to overcome the difficulties that abound in their real life. Therefore, it is a must for parents to cultivate the independence which helps their children easily conquer frustration and depression, To conclude, itu2019s essential for us to dispose of the problem of childrenu2019s independence timely and effectively. Parents should help children develop strong independence and the abilities needed in the future. Only in this way can they be ready to confront any challenges in the society of fierce competition. 2010-06 Due Attention Should Be Given to Spelling Nowadays fewer and fewer students pay attention to their word-spelling. According to a recent survey, there is a dramatic increase in the number of students who can only imitate the pronunciation of a word but be incapable of spelling it. In this essay I will discuss the factors of this phenomenon and offer my own view on it. There are a number of factors that can be accountable for this situation. One of the most common factors is that fewer and fewer students need to write English essays. Besides, the goal of most students to learn English is to speak it and pass the examination which means they just need to select the similar words according to the listening materials and passages. Perhaps the most contributing factor is the wide use of electronic devices such as e-dictionaries and computers and students no longer need to correct the words by themselves. As far as Iu2019m concerned, I firmly argue that we need to attach great importance to word-spelling. To the students, they should write English as much as they can. Meanwhile, to the teachers, the dictations should be reinforced in the class. 2009-12 Create a Green Campus In recent years, extravagance and waste have become increasingly serious in some of the university campus. We can see that papers, bottles and cans are thrown away after use; food is wasted just because of its poor taste; clothes are discarded simply owning to their old fashion. As a consequence, people in mounting numbers put great emphasis on creating a green campus. There are at least two criteria to distinguish what is green campus. On the one hand, natural resources must be conserved and made full use of, for example, we, as college students, should take the wise use of papers and second-hand textbook into account. On the other hand, education to build up thrift habits must be prompt by relevant departments and professionals at various levels. Accordingly, it is necessary for us to take effective steps. For one thing, university authorities should respond with the demand for more natural resources, such as water, electricity, and so on. For another, we should enhance the awareness of college students that creating a green campus is of utmost significance to both our society and ourselves. daily courses. There are many factors that may account for it, and the following are the most conspicuous aspects. To start with, many students want to get another degree besides their own, so that they can have more competence when they seek for a job. Furthermore, as for me, I donu2019t care about degree or job, and I want to obtain some necessary skills to make my college life worthwhile. Finally, some students want to learn anything that is different from what they are learning now. The science students , for example, want to know about Shakespeare while the art students want to tell how a vehicle works and how to deal with it when it breaks down. On the whole, the phenomenon is one of the results of multi-demand of the employment market. There is still a long way for us to improve the elective itself, but as a student myself, I find it rewarding and interesting. 2007-06 An Announcement to Welcome Students to Join A Club Welcome to English Club! It could serve as a platform to show your outstanding abilities and help you develop a range of great skills. You can be involved in a variety of activities including staging musical dramas, holding group discussions and watching Oscar-winning movies. These extracurricular activities could offer you ample opportunities. First, your active participation is helpful to strengthening the sense of responsibility and managing interpersonal relations. Second, various activities organized by us could raise your level of proficiency in English. A good command of English empowers you to enjoy a competitive edge over your peers. You can file a written application to our office or email us via bonoo@diandian.net. The deadline for entries is Sept. 25th. Come on, join us now. 2006-12 Spring Festival Gala on CCTV The Spring festival gala has been held in China for over two decades, which seems to have been an indispensable company during the traditional New Yearu2019s Eve for a great number of people, who appear to be accustomed to enjoying the sights and sounds of a brilliant feast, while gathering with their beloved family. However, an increasing number of people have voiced different opinions towards it, as more diverse life styles have emerged nowadays. Some prefer to go to a fancy restaurant to enjoy a gourmet meal; some intend to go on a vacation to an incredibly exotic destination for a novel and thorough relaxation; others may have even more post-modern notions, like go bunging, hiking, or cycling for entirely new different experiences, forgetting all about the Spring Festival. To me, the Evening Gala is supposed to be here to stay. It may not remain a must for all people, but it can bring us a strong sense of festivity and serve as an alternative among the variety of holiday activities. Besides, with such a gathering, family members will have a perfect opportunity to enjoy more fun and happiness, for nowadays most people are so engaged in their daily business that they can rarely find any extra time to stay with their family, which, if not properly adjusted, might add further to the already worsening situation of Chinese families. 2002-1 A Letter to University President about the Canteen service on Campus January 12th , 2002 Dear Mr. President, Iu2019m very lucky to attend this world-famous university, but Iu2019m not content with the canteen service on campus.

I study in the No.I middle school,where there are three grades and thirty-two classes.It is not big but very beautiful.In the center of the school there is a new teaching building,which is very clean and beautiful.The lab building and the library are to the east of the new building.There all kinds of book in the library.You can enioy them as many as you like.South of the new building lies a playground and it"s very big.On the playground,you can have sports such as football.basketball.You"d better play basketball as there are four basketball grounds in our school,You can enjoy yourself very much.There are many trees in our school.Grass is everywhere.In front of the new building there are two gardens in which,there are flowers of all colours.We are studying hard in our school,Our life is happy and intcrcsting.I love our school very much.

全诗的意思：三万里长的黄河奔腾向东流入大海，五千仞高的华山耸入云霄上摩青天。中原人民在胡人压迫下眼泪已流尽，他们盼望王师北伐盼了一年又一年。

As is known to us all, the surrounding has a great impact on our study and lives. In recent years, creating a green campus has been a common and popular goal for most universities or colleges. Creating a green campus has a great influence on students because most students spend their much time in campus.众所周知，环境的对我们的学习和生活有很大的影响。近年来，创建绿色校园已经成为大多数的大学或学院是普遍存在的目标了。创建绿色校园对学生有很大的影响，因为大多数学生的大部分时间都是在校园。However, in my opinion, to create green campus, what we need to do is not only to plant more trees and grasses to beautify our campus"s environment but also to create an energy-efficient and resource-cycled campus. Everyone on campus should be informed to form the habit of using resources properly and saving energy. In addition, the institutions should encourage students to use resources circularly.然而，在我看来，创建绿色校园，我们需要做的是不仅要种植更多的树和草来美化我们的校园环境也创造了一个节能和资源循环的校园。校园里的每一个人都应该被要求形成节约能源资源的习惯。此外，学校应鼓励学生资源循环利用。In a word, creating a green campus needs us to make joint efforts. And we can achieve it by doing pieces of small matters in daily life, such as turning off the light when leaving.总之，创建绿色校园需要我们共同的努力。我们可以在日常生活中的小事做起，如离开的时候关灯。

秋夜将晓出篱门迎凉有感二首 陆游迢迢天汉西南落，喔喔邻鸡一再鸣。壮志病来消欲尽，出门搔首怆平生。三万里河东入海，五千仞岳上摩天。遗民泪尽胡尘里，南望王师又一年。译文迢迢万里的银河朝西南方向下坠，邻家的公鸡喔喔叫个不停。疾病几乎把报国壮志消磨殆尽，出门四望不禁手搔白发抱憾平生。三万里长的黄河奔腾向东流入大海，五千仞高的华山耸入云霄触青天。中原人民在胡人压迫下眼泪已流尽，他们盼望王师北伐盼了一年又一年。

As is known to us all, the surrounding has a great impact on our study and lives. In recent years, creating a green campus has been a mon and popular goal for most universities or colleges. Creating a green campus has a great influence on students because most students spend their much time in campus. However, in my opinion, to create green campus, what we need to do is not only to plant more trees and grasses to beautify our campus"s environment but also to create an energy-efficient and resource-cycled campus. Everyone on campus should be informed to form the habit of using resources properly and saving energy. In addition, the institutions should encourage students to use resources circularly. In a word, creating a green campus needs us to make joint efforts. And we can achieve it by doing pieces of *** all matters in daily life, such as turning off the light when leaving.

As is known to us all, the surrounding has a great impact on our study and lives. In recent years, creating a green campus has been a common and popular goal for most universities or colleges. Creating a green campus has a great influence on students because most students spend their much time in campus. 众所周知，环境的对我们的学习和生活有很大的影响。近年来，创建绿色校园已经成为大多数的大学或学院是普遍存在的目标了。创建绿色校园对学生有很大的影响，因为大多数学生的大部分时间都是在校园。 However, in my opinion, to create green campus, what we need to do is not only to plant more trees and grasses to beautify our campusu2019s environment but also to create an energy-efficient and resource-cycled campus. Everyone on campus should be informed to form the habit of using resources properly and saving energy. In addition, the institutions should encourage students to use resources circularly. 然而，在我看来，创建绿色校园，我们需要做的是不仅要种植更多的树和草来美化我们的校园环境也创造了一个节能和资源循环的校园。校园里的每一个人都应该被要求形成节约能源资源的习惯。此外，学校应鼓励学生资源循环利用。 In a word, creating a green campus needs us to make joint efforts. And we can achieve it by doing pieces of small matters in daily life, such as turning off the light when leaving. 总之，创建绿色校园需要我们共同的努力。我们可以在日常生活中的小事做起，如离开的时候关灯。

也。秋夜将晓出篱门迎凉有感作者：陆游三万里河东入海，五千仞岳上摩天。遗民泪尽胡尘里，南望王师又一年。诗题意思：秋天的夜里，天快要亮的时候，走出篱笆门，忽然对面吹来一阵凉风，心中产生一股伤感，于是写下这首诗。