已知3^m=6,27^n=2,求3^2m-2n的值

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已知3^m=6,27^n=2,求3^2m-2n的值
已知3^m=6,27^n=2,求3^2m-2n的值

已知3^m=6,27^n=2,求3^2m-2n的值
3^(2m-2n)
=(3^2m)/(3^2n)
=[(3^m)^2]/[(27^n)^(2/3)]
=(6^2)/[2^(2/3)]
=36/4^(1/3)
=9*(16)^(1/3)

3^m=6
27^n=(3^3)^n=(3^n)^3=2,即有3^n=2^1/3
3^2m-2n=(3^m)^2/(3^n)^2=6^2/(2^1/3)^2=36/2^2/3=18*2^1/3

36-6*log2 3

22.6785789

3^m=6
3^2m=36
27^n=2
3^3n=2

3^(2m-3n)(3n选我,2n找别人答案)
=3^2m/3^3n
=36/2
=18