(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
人气:485 ℃ 时间:2020-04-12 14:43:25
解答
(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
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