解不等式4^x+5*2^x<=6

4^x + 5*2^x <= 6

(2^x)^2 + 5*2^x - 6 <= 0

(2^x + 6)(2^x - 1) <= 0

2^x + 6 >= 0 ........................x为任意实数
2^x - 1 <= 0 ........................x <= 0

综合后，x <= 0

2^x + 6 <= 0
2^x - 1 >= 0

此种无解.

所以,该不等式的解集为: x <= 0

^啥意思？我帮你回答

设2^x=y
y^2+5y-6<=0 因式分解 (y+6)(y-1)<=0 所以1<=y<=6即1<=2^x<=6，
开方：1<=x<=根号6

令2^x=X，则X^2+5X<=6得出-5<=X<=1，注意到2^x>0,所以为0<=X<=1

对于2^x这个函数来说，为单调递增，所以x<=0
刚才算错，现在改过来