(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

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/04/28 21:04:15

(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）求值

(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

如果log以3为底[log以4为底（log以5为底的a次方）]等于log以4为底[log以3为底（log以5为底的b次方 log以2为底5为真数与log以5为底8 计算：（log以4为底3的对数+log以8为底3的对数）（log以3为底2的对数+log以9为底2的对数）- log以½ log以2为底的（log以3为底的（log以4为底的x))=log以3为底的（log以4为底的（log以2为底的y))= 计算log以8为底16+log以2为底3*log以3为底2=? 计算(log以2为底的3+log以4为底的9+log以8为底的7+……+log以2^n为底的3^n)*log以9为底^n log以2为底25乘log以3为底8乘log以5为底9=?用换底公式求 log以2为底25的对数乘以log以3为底4的对数乘以log以5为底9的对数 log以2为底25的对数乘log以3为底4的对数乘log以5为底9的对数=? log以2为底25的对数+log以3为底4的对数+log以5为底9的对数 log以4为底数27的对数乘log以5为底8的对数乘log以3为底25的对数 ﹙log以2为底5的对数+log以4为底125的对数﹚乘以﹙log以3为底2的对数/log以根号3为底的5的对数﹚