对数方程log2(x-1)=log4 x,如何化成(x-1)²=x

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对数方程log2(x-1)=log4x,如何化成(x-1)²=x对数方程log2(x-1)=log4x,如何化成(x-1)²=x对数方程log2(x-1)=log4x,如何化成(x

对数方程log2(x-1)=log4 x,如何化成(x-1)²=x
对数方程log2(x-1)=log4 x,如何化成(x-1)²=x

对数方程log2(x-1)=log4 x,如何化成(x-1)²=x
log2(x-1)=log4 x,
则 x>1
log2(x-1)=log2 √x
x-1=√x
(x-1)²=x

设 log2(x-1)= log4 x = t

则 2^t = x-1 => (2^t)(2^t) = (x-1)² => 4^t =(x-1)²
又 4^t = x
所以 (x-1)²=x

log(x-1)=0.5log2 x 2log(x-1)=log2 x log(x-1)^2=log2 x (x-1)^2=x (x>1)