For what value does x does 3^2x= g^3x-4A)1B)2C)3D)4

The question has an error because the letter g does not make sense in the context.

I will assume that the g is really the number 9.

In that case, the equation to solve would be:

[tex] 3^{2x} = 9^{3x-4} [/tex]

You can solve for x following these steps:

1) make      [tex]9=3^2[/tex]

=>

[tex] 3^{2x} = 3^{2(3x-4)} [/tex]

2) Given that the basis are equal the exponents have to be equal =>

2x = 2(3x - 4)

3) Solve:

2x = 6x - 8

6x - 2x = 8

4x = 8

x = 8/4

x = 2 which is the option B) which leads me to think that a 9 instead of g in the equation should be right.

Under that assumption, the answer is the option B) x = 2.