对数与对数运算二VIP免费

指数式与对数式互化：ax=Nx=logaN对数恒等式(或对数的性质)：(1)log1a(2)logaa(3)lognaalog(4)aNa(5)logmnaa0与负数没有对数当a>0,且a≠1时,01nNnm1.设logaM＝p,logaN＝q,试用p,q表示:loga(M·N)解:log∵aM＝p∴M＝aplogaN＝q∴N＝aq∴loga(M·N)＝loga(ap·aq)＝logaap+q=p+q即即loglogaa((MM··NN))＝＝loglogaaMM＋＋loglogaaNN证明:设logaM＝p,logaN＝q,则M＝ap,N＝aqqpaaaNMqpaqpaalogloglogNMNMaaalogloglog即NMNMaaalogloglog2.证明:(1)log()loglogaaaMNMNNMNMaaalogloglog)2(MnManaloglog)3(对数的运算法则两数的积的对数,等于各数的对数的和当a＞0,且a≠1,且M＞0,N＞0时,有：两数的商的对数,等于被除数的对数减去除数的对幂的对数,等于幂指数乘以幂的底数的对数公式辩析:下列式子中正确的个数有(),其中a＞0且a≠1,x＞0,y＞0.(1)log()loglogaaaxyxy(2)logloglogxaaayxy(3)(log)lognaaxnx1(4)loglogaaxx(A)0个(B)1个(C)2个(D)3个例1设r=logax,s=logay,t=logaz,a>0,且a≠1,试用r,s,t表示下列各式,r>0,s>0,t>0.(1)logaxyz23(2)logaxyzzxyaalog)(logzyxaaalogloglogtsr32log)(logzyxaa31212logloglogzyxaaatsr31212例1设r=logax,s=logay,t=logaz,a>0,且a≠1,试用r,s,t表示下列各式,r>0,s>0,t>0.(1)logaxyz23(2)logaxyz(3)logxytsrtsr31212tyxlog令xyyaxalogloglogtxytaaxyloglogxtyaaloglogxyyaaxlogloglogtsyxlog换底公式：logloglogaxayyxloglognmaambbn推论：loglog1abba(a>0,且a≠1,x>0且x≠1,y>0)例2计算下列各式:18lg7lg949lg14lg)2(25lg20lg)1(100cbacbacba212:.643,0,0,0)3(求证且设1.设a=lg2,b=lg3,试用a,b表示下列各式:(1)lg6(2)lg12(3)lg325(5)log188(4)log27巩固练习:ab2ab52aba21aba25log264log6)1.(25148.1lg10lg3lg2lg)2(.2222,3log.4332的值求设xxxxx.)21(2,10054.3的值求设baba