數學次方數

題目是否如此 :
2^(2x-3) - (3/2)(2^x) = -2^2

2009-11-10 11:55:53 補充：
先讓 Ivanray12345 知識友作答, 如果5分鐘內他不再補充, 我才給你解答。

2009-11-10 12:08:45 補充：
既然 Ivanray12345 知識友不再補充, 讓我給你解答。

2^(2x-3) - (3/2) (2^x) = -2^2
[2^(2x)] (2^-3) - (3/2) (2^x) = -4
[2^(2x)] / (2^3) - (3/2) (2^x) + 4 = 0
[(2^x)^2] / 8 - (3/2) (2^x) + 4 = 0
(2^x)^2 - 12 (2^x) + 32 = 0
( 2^x - 4 ) ( 2^x - 8 ) = 0
2^x - 4 = 0 or 2^x - 8 = 0
2^x = 4 or 2^x = 8
2^x = 2^2 or 2^x = 2^3
x = 2 or x = 3

2^(2x-3) - (3/2)(2^x) = -2^2
(1/8)2^2x - (3/2)(2^x) = -4
設 y = 2^x
(1/8)y^2 - (3/2)y = -4
y^2 - 12y + 32 = 0
(y-4)(y-8) = 0
y =4, 或 y= 8
2^x = 4
2^x =2^2
∴ x = 2

2^x= 8
2^x =2^3
∴ x = 3

yes.You guess right!

what is ^????????????