解方程. 越详细越好.需要解析

解：2的X+2方-2的X方=96
2^x * 2^2 -2^x=96
3* 2^x=96
2^x=32
x=5

2lgx=lg(x+12)
lgx^2=lg(x+12)
x^2=x+12
x=-3或4

lg(x+5)+lg（x+3）-lg4=lg(2x-9)
lg[(x+5)*(x+3)]=lg[(2x-9)*4]
这题你确定题目没错？

-5＜2x-3＜5
-1＜x＜4

(1) 2^(x+2) - 2^x=4*2^x- 2^x=3*2^x= 96==3*2^5
===> x=5
(2)2lgx=lg(x+12) ==> lg x^2= lg(x+12) ==> x^2=x+12
==> x=4 x= -3
(3) lg(x+5)+lg(x+3)-lg4= lg(2x+9) ==> lg(x+5)(x+3)+lg4=lg(2x+9)
==> lg [(x+5)(x+3)/4]=lg(2x+9)
===> (x+5)(x+3)/4=2x+9 ==> x^2 = -51
当x 为复数时有解
(4) |2x-3|<=5 ==> 2x-3<=5 或2x-3>= -5
==> x<=4 或 x>=-1 即 1<= x <= 4