Question

Solve the exponential equation. 53x + 4 = 55x (1 point) Responses x = 5 x = 5 x = 2 x = 2 x = 1 x = 1 x = 4

Answer 1

To solve the exponential equation \( 5^{3x + 4} = 5^{5x} \), we can set the exponents equal to each other since the bases are the same:

\[
3x + 4 = 5x
\]

Now, we can rearrange this equation to isolate \( x \):

\[
4 = 5x - 3x
\]

\[
4 = 2x
\]

Now, divide both sides by 2:

\[
x = 2
\]

Thus, the solution to the equation \( 5^{3x + 4} = 5^{5x} \) is:

\[
\boxed{2}
\]

So, the correct response is \( x = 2 \).