We have to solve 9^2x = 27^(3x-2)

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

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

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

As the base is the same on both the sides we can equate the exponent.

4x = 9x - 6

=> 5x = 6

=> x = 6/5

Therefore **x = 6/5**

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**