求[log(2)9+log(4)9+log(8)27+……+log(2^n)3^n]*log(9)n次根号32(n∈N*
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求[log(2)9+log(4)9+log(8)27+……+log(2^n)3^n]*log(9)n次根号32(n∈N*)的值.要具体过程,
[log(2)9+log(4)9+log(8)27+……+log(2^n)3^n]*log(9)n次根号32
=[lg3^2/lg2+lg3^2/lg2^2+lg3^3/lg2^3+.+lg3^n/lg2^n]*lg2^(5/n)/lg3^2
=(2+1+1+.+1)*2(5/n)*lg3/lg2*lg2/lg3
=10(n+1)/n
=[lg3^2/lg2+lg3^2/lg2^2+lg3^3/lg2^3+.+lg3^n/lg2^n]*lg2^(5/n)/lg3^2
=(2+1+1+.+1)*2(5/n)*lg3/lg2*lg2/lg3
=10(n+1)/n
计算(log以2为底的3+log以4为底的9+log以8为底的7+……+log以2^n为底的3^n)*log以9为底^n
(log2 3+log4 9.+log8 27+.+log(2^n底)(3^n))log9 n次根号32
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