Question

（log以2为底125的对数+log以4为底25+log8 5 ）（log5 2 +log25 4+log125 8 ）求解啊~~

后面一样的格式。。

Answer 1

解

Answer 2

解：先用对数的换底公式，(以10为底) 再应用对数的运算法则
原式=(lg125/lg2+lg25/lg4+lg5/lg8)(lg2/lg5+lg4/lg25+lg8/lg125)
=(3lg5/lg2+2lg5/2lg2+lg5/3lg2)(lg2/lg5+2lg2/2lg5+3lg2/3lg5)
=(3lg5/lg2+lg5/lg2+lg5/3lg2)×3lg2/lg5
=9+3+1
=13

Answer 3

(log₂125+log₄25+log₈5)(log₅2+log₂₅4+log₁₂₅8)
=[(log₅125)(/log₅2)+(log₅25)/(log₅4)+1/log₅8)(log₅2+log₅2+log₅2)
=[(log₅125)/(log₅2)+(log₅25)/(2log₅2)+1/(3log₅2)](3log₅2)
=[log₅125+(log₅25)/2+(1/3)]×3
=[3+1+(1/3)]×3=13