对数与对数运算一VIP免费

2.2.1.1对数及对数的运算(一)x3=8,则x=;x3=9,则x=;2392x=16,则x=;3x=8,则x=;2x=9,则x=;4log38log2910x=N,则x=;log10Nax=N,则x=;logaN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,记做x=logaN指数式对数式真数N>0即,0与负数没有对数以a为底N的对数对数的真数对数的底数当a>0,且a≠1时,ax=Nx=logaN;lognaalog0.58=;基础练习:log232=;loga1=;logaa=;对数恒等式,a>0且a≠1,(或对数的性质):5-301n;log1aa-1;=log1aa-1;lognaanlog10NlogeN常用对数：自然对数：其中e是无理数,称为自然对数的底,e≈2.71828‥‥‥=lgN=lnN例1将下列指数式化为对数式,对数式化为指数式.4(1)564512(4)log164(5)lg0.012(6)ln102.30371(2)21281(3)()5.733m54log645112827log13log5.73m41()1622100.0110303.2e2364x例2求下列各式中x的值.642(1)log3x(2)log86x(3)lg100x2(4)lnex233(4)23()3411668x68x168136(2)210log10x或2logexe或2x2x10100x2logexe2xeex100log102=例2求下列各式中x的值.1)(loglog)5(25x0)]lg[ln(log)6(2x5log2x3225x1)ln(log2xex2logex2例31.基础计算：91(1)log8129log9239log3432:logmnanam结论329log9324325log5634239log(9)25log)5(34527log)4(331()23(23)log1)3—2(log)2()3+2(27log)3(9333log=232=3log2=3333log=23log×23=323=..2能力与提高5log13333log42225log12)2(15log3)2(33165325165295log3lg33log45log1223)21(102333lg)10(归纳：1.对数的定义:log(0,1)xaaNxNaa2.对数的性质:(1)0与负数没有对数;(2)1的对数是0,即loga1=0;logNaaNlog1aalogaNaNlogmnanam