Question
Given the exponential equation 5x=625 , solve for the value of x that makes the equation true.(1 point)
Answers
GPT-4o mini
To solve the exponential equation \( 5^x = 625 \), we first express \( 625 \) as a power of \( 5 \).
We can find this by noticing that:
\[
625 = 5 \times 5 \times 5 \times 5 = 5^4
\]
Now, we can rewrite the original equation:
\[
5^x = 5^4
\]
Since the bases are the same, we can set the exponents equal to each other:
\[
x = 4
\]
Thus, the solution is:
\[
\boxed{4}
\]
We can find this by noticing that:
\[
625 = 5 \times 5 \times 5 \times 5 = 5^4
\]
Now, we can rewrite the original equation:
\[
5^x = 5^4
\]
Since the bases are the same, we can set the exponents equal to each other:
\[
x = 4
\]
Thus, the solution is:
\[
\boxed{4}
\]