对数的换底公式怎么用具体举例换底公式log怎么换成lg和ln

\u6362\u5e95\u516c\u5f0f\u600e\u4e48\u7528\uff1f\u53ef\u4ee5\u4e3e\u51e0\u4e2a\u4f8b\u5b50\u5417

\u6362\u5e95\u516c\u5f0f\u600e\u4e48\u7528\u5462\uff1f

(log以2为底125＋log以4为底25＋log以8为底5）（log以5为底2＋log25为底4＋log以125为底8)
=(lg125/lg2+lg25/lg4+lg5/lg8)(lg2/lg5+lg4/lg25+lg8/lg125)
=(3lg5/lg2+lg5/lg2+1/3lg5/lg2)(lg2/lg5+lg2/lg5+lg2/lg5)
=13/3lg5/lg2*3lg2/lg5
=13/3*3
=13

log以a为底b=lgb/lga

例如：log以2为底8的对数=lg8/lg2=log以3为底8的对数/log以3为底2的对数，等等