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