9^2x = 27^(3x-2) find x.

9^2x = 27^(3x-2)

To solve for
x, we will use the exponent properties to find x.

First we
will rewrite the bases as powers of prime numbers.

We know
that:

9 = 3^2

27 =
3^3

Let us
substitute.

==> 3^2)^2x =
(3^3)^(3x-2)

Now we know that x^a^b =
x^ab

==> 3^(2*2x) =
3^(3*(3x-2)

==> 3^(4x) =
3^(9x-6)

Now that the bases are equal, then the powers are
equal too.

==> 4x = 9x
-6

==> -5x =
-6

==> x =
6/5