SOLUTION: I'm very much stuck on this problem. I'm not sure if this is in the right section, but I hope someone can help. (2^x)^(x+3)=1/4 If I try to simply this using the rules of ex

Question 379549: I'm very much stuck on this problem. I'm not sure if this is in the right section, but I hope someone can help.
(2^x)^(x+3)=1/4
If I try to simply this using the rules of exponents, I get..
2^(x^2+3x)=1/4
How can I possibly simplify this since x^2 and 3x are not like terms? I thought about making it a logarithm to make it no longer an exponent, but I still can't figure out how I would solve for x. Please help!

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
2^(x^2+3x)=1/4
2^(x^2+3x)=1/2^2
2^(x^2+3x)=2^-2
..
x^2+3x=-2
x^2+3x+2=0
x^2+2x+x+2=0
x(x+2)+1(x+2)=0
(x+2)(x+1)=0
x=-1 OR x=-2

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