log27^4*log8^9详细解法

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log27^4*log8^9详细解法
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log27^4*log8^9详细解法
log27^4*log8^9详细解法

log27^4*log8^9详细解法
log27 4*log8 9
=log(3³) (2²)*log(2³) (3²)
=(2/3)log3 2*(2/3)log2 3
=(2/3)*(2/3)log3 2*log2 3
=4/9

log27(4) ×log8(9)
=(lg4/lg27)×(lg9/lg8)
=[lg(2²) /lg(3³)]×[lg(3²)/ lg(2³)]
=[(2lg2)/(3lg3)]×[(2lg3)/(3lg2)]
=(2/3)×(2/3)×(lg2/lg3)×(lg3/lg2)
=4/9