SOLUTION: Could someone show me the steps involved in solving this equation: 9^2x * (1/3)^(x+2) = 27 * (3^x)^-2 The book says that the answer is 1 but I get an answer of 1/5. I solve t

Question 874625: Could someone show me the steps involved in solving this equation:
9^2x * (1/3)^(x+2) = 27 * (3^x)^-2
The book says that the answer is 1 but I get an answer of 1/5. I solve the problem all the way down to:
3^(3x+2) = 3^(3-2x) then I set the exponents equal to each other and solve for x: 3x + 2 = 3 - 2x and I get 1 for and answer. I can't figure out how they get 1 for an answer for x.
Could someone please help.
Thanks.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
not
3^(3x+2) = 3^(3-2x)
but
3^(2-x) x = 3^(3-2x)
2-x=3-2x
-1=-x
x=1

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