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x^2 / 9^x = 9

x^2 = (9^x)(9^1)

x^2 = 9^(x + 1)

By observation and logic, the only possible answer is x = -1.

first multiply each side by 9^x

you get: 3x^2 = 27 x 9^x

now divide both sides by 3

you will get

x^2= 9 x 3^x

now you have to bring that x down so you have to take log base 3 of 3 to both sides

log 3 (x^2) = log 3 (9) log 3 (3^x)

log 3 (x^2) = 2x

divide 2 on both sides

x = log base 3 (x^2) / 2

hope i did this right iam very tired its nearly 3 am

you get: 3x^2 = 27 x 9^x

now divide both sides by 3

you will get

x^2= 9 x 3^x

now you have to bring that x down so you have to take log base 3 of 3 to both sides

log 3 (x^2) = log 3 (9) log 3 (3^x)

log 3 (x^2) = 2x

divide 2 on both sides

x = log base 3 (x^2) / 2

hope i did this right iam very tired its nearly 3 am

You did it wrong, the answer is -1.

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