Question

solve the exponential equation.
$5^x = 625$
$x = \square$ (simplify your answer. type an integer or a decimal.)

Explanation:

Step1: Express 625 as a power of 5

We know that \(5\times5\times5\times5 = 5^4\), so \(625 = 5^4\).
The equation \(5^x = 625\) becomes \(5^x = 5^4\).

Step2: Use the property of exponents

If \(a^m=a^n\) (where \(a>0,a
eq1\)), then \(m = n\).
Here \(a = 5\), \(m=x\) and \(n = 4\), so \(x=4\).

Answer:

\(4\)