已知3^m=6,9^n=2,求3^(2m-4n+1)
已知3^m=6,9^n=2,求3^(2m-4n+1)
参考答案:解:由3^m=6,9^n=2得
m=log(3)6;(底数为3,真数为6的对数)
n=log(9)2=(1/2)·log(3)2(底数为3,真数为2的对数)
那么, 2m-4n+1
=2·log(3)6-2·log(3)2+1
=2·[log(3)6-log(3)2]+1
=2·log(3)3+1
=3
因此,3^(2m-4n+1)
=3^3
=27
已知3^m=6,9^n=2,求3^(2m-4n+1)
参考答案:解:由3^m=6,9^n=2得
m=log(3)6;(底数为3,真数为6的对数)
n=log(9)2=(1/2)·log(3)2(底数为3,真数为2的对数)
那么, 2m-4n+1
=2·log(3)6-2·log(3)2+1
=2·[log(3)6-log(3)2]+1
=2·log(3)3+1
=3
因此,3^(2m-4n+1)
=3^3
=27