Given:
[tex]5^{2x+1}=125[/tex]
We will solve the exponential equation to find (x)
First, we will make a prime factorization of 125
125 = 5 * 5 * 5 = 5³
So, the given equation can be written as follows:
[tex]5^{2x+1}=5^3[/tex]
both sides have a base of (5), so the exponents are equal
we can write the following equation:
[tex]2x+1=3[/tex]
Solve the equation to find (x)
[tex]\begin{gathered} 2x=3-1 \\ 2x=2 \\ x=\frac{2}{2}=1 \end{gathered}[/tex]
So, the answer will be x = 1
