2^(2x-3) - 3 x 2^(x-2)+1=02logx25-3log25x=1

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2^(2x-3) - 3 x 2^(x-2)+1=02logx25-3log25x=1
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2^(2x-3) - 3 x 2^(x-2)+1=02logx25-3log25x=1
2^(2x-3) - 3 x 2^(x-2)+1=0
2logx25-3log25x=1

2^(2x-3) - 3 x 2^(x-2)+1=02logx25-3log25x=1
1、1/8(2^X)^2-3/4(2^X)+1=0
(2^X)^2-6×2^X+8=0
(2^X-2)(2^X-4)=0
∴2^X-2=0或2^X=4,
∴X=1或X=2.
2、设logX(25)=Y,
于是原方程化为：
2Y-3/Y=1
2Y^2-Y-3=0
(2Y-3)(Y+1)=0,
Y=3/2或Y=-1,
logX(25)=3/2,logX(25)=-1,
X=125或X=1/25.

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