求log3^2*log4^9的值求log3^2*log4^9的值

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求log3^2*log4^9的值
求log3^2*log4^9的值

log(a)(b)表示以a为底的b的对数.
所谓的换底公式就是log(a)(b)=log(n)(b)/log(n)(a).
log3^2*log4^9=(1g2/1g3)*(1g9/1g4)
=(1g2/1g3)*(2*1g3/2*1g2)
=(1g2/1g3)*(1g3/1g2)
=1

log3^2*log4^9=log3^2*（2/2)*log2^3=1

log3^2*log4^9
=log3^2*2*log4^3
=log3^2*2*1/2*log2^3
=1

1，log4^9=log3^2分之一

用换底公式。
log3^2*log4^9=(1g2/1g3)*(1g9/1g4)
=(1g2/1g3)*(2*1g3/2*1g2)
=(1g2/1g3)*(1g3/1g2)
=1

1

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