若f(x)=2的x-2方，f(log以4为底的x)=1/5,则x=

显示全部楼层 · 2012-1-19 00:34:50

我把log以4为底的x 写成lo4gx方便点令y=lo4gx，则f(y)=5^-1有f(y)=2^(y-2)=5^-1，两边同取对数lo4g,则 (y-2)lo4g2=-lo4g5
(y-2)lo4g4^(1/2) =-lo4g5即 y/2=1-lo4g5=lo4g(4/5)y=lo4g(4/5)^2 代入上式y=lo4gx中得lo4g(4/5)^2=lo4gxx=16/25...

千问 · 2012-1-19 00:34:50

解：（log以4为底的X=1/2log以2为底的X）
f（log以4为底的X）=f（1/2log以2为底的X）=2^（1/2log以2为底的X）-2
=【2^（log以2为底的X）】^(1/2)-2=X^(1/2)-2
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