用换底公式求log(2)25乘log(3)4乘log(5)9的值

问题描述:

用换底公式求log(2)25乘log(3)4乘log(5)9的值

log(2)5=log(3)5/log(3)2
log(5)3=log(3)3/log(3)5=1/log(3)5
log(2)25乘log(3)4乘log(5)9
=(2*log(2)5)(2*log(3)2)(2*log(5)3)
=8*log(3)5*log(5)3
=8*log(3)5*1/log(3)5
=8