(log3^2 + log9^4)×(log4^3 + log8^3)

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(log3^2 + log9^4)×(log4^3 + log8^3)

(log3^2 + log9^4)×(log4^3 + log8^3)
(log3^2 + log9^4)×(log4^3 + log8^3)

(log3^2 + log9^4)×(log4^3 + log8^3)
首先解释一下ln4=2ln2
底数也有类似规律
log4^3=1/2(log2^3)
所以
(log3^2 + log9^4)×(log4^3 + log8^3)
= (log3^2 + log3^2)×((1/2)log2^3 + (1/3)log2^3)
=5/3

(log3 2+log9 4)*(log4 3+log8 3)
=(lg2/lg3+lg4/lg9)*(lg3/lg4+lg3/lg8)
=(lg2/lg3+2lg2/2lg3)*(lg3/2lg2+lg3/3lg2)
=(3lg2/lg3)*(lg3/2lg2+lg3/3lg2)
=(3lg2/lg3)*(3lg3/6lg2+2lg3/6lg2)
=(3lg2/lg3)*(5lg3/6lg2)
=3*5/6
=5/2