Question

For what value of x does 3²x _ g³x-4?

Answer 1

`x=2`

Explanation:

I believe your question is:

For what value of
`x` does
`3^(2x)=9^(3x-4)`?

—

First, rewrite
`9` as
`3^2`:

`3^(2x)=(3^2)^(3x-4)`

Then, use exponentiation to apply the
`(a^b)^c=a^(bc)` rule:

`3^(2x)=3^(2(3x-4))`

Rewrite the expression as a non-exponential one since the bases (
`3`) are equal on both sides:

`2x=2(3x-4)`

Distribute the
`2`:

`2x=6x-8`

Subtract
`6x` from both sides:

`-4x=-8`

Divide both sides by
`-4`:

`x=2`