log(3)5加上log(5)3减去log(3)15乘以log(5)15等于多少

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log(3)5加上log(5)3减去log(3)15乘以log(5)15等于多少
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log(3)5加上log(5)3减去log(3)15乘以log(5)15等于多少
log(3)5加上log(5)3减去log(3)15乘以log(5)15等于多少

log(3)5加上log(5)3减去log(3)15乘以log(5)15等于多少
log(3)15*log(5)15
=log3(3*5)*log5(3*5)
=(log3(3)+log3(5))*(log5(3)+log5(5))
=(1+log3(5))*(log5(3)+1)
=1+log3(5)*log5(3)+log3(5)+log5(3)
=1+(ln3/ln5)*(ln5/ln3)+log3(5)+log5(3)
=2+log3(5)+log5(3)
log(3)5+log(5)3-log(3)15*log(5)15=-2

用换底公式变为lg5/lg3+lg3/lg5-(lg15)^2/(lg3*lg5)
通分化简有((lg5)^2+(lg3)^2-(lg15)^2)/(lg3*lg5)
因为lg5+lg3=lg15
化简上式可得-2