Question

Solve the exponential equation 3 ^ 4 = 3 ^ (-2x) (1 point) x = 2; x = 3; x = - 2; x = 4

Answer 1

To solve the exponential equation \( 3^4 = 3^{-2x} \), we can set the exponents equal to each other since the bases are the same:

\[
4 = -2x
\]

Now, we can solve for \( x \):

\[
-2x = 4
\]

Dividing both sides by -2:

\[
x = \frac{4}{-2} = -2
\]

So, the solution to the equation is:

\[
\boxed{-2}
\]