4.18-4/方程log(2)[(4^x)+1]=x+log(2)[2^(x+3)-6]的解是（）？

log(2)[(4^x)+1]=x+log(2)[2^(x+3)-6]
log(2)[(4^x)+1]=log(2)[2^x]+log(2)[2^(x+3)-6]
log(2)[(4^x)+1]=log(2){[2^x]*[2^(x+3)-6]}
4^x + 1 = 2^x * [2^(x+3)-6]
4^x + 1 = 4^x * 8 - 6 * 2^x
7 * 4^x - 6 * 2^x - 1 = 0
(7 * 2^x + 1) * (2^x - 1) = 0
2^x = -1/7 无解，或
2^x = 1, x = 0

于是，解 x=0.

思路，把等式两边变换成相同的底数，然后方程等价于真数相等。