Use the like bases property to solve the equation \( 3125^{x}=625 \) \( x=\square \) Question Help: Video

To solve the equation \( 3125^{x} = 625 \), start by expressing both numbers with the same base. Notably, \( 3125 = 5^5 \) and \( 625 = 5^4 \). Rewriting the equation, we have \( (5^5)^{x} = 5^4 \). Applying the power of a power property, this simplifies to \( 5^{5x} = 5^4 \). Since the bases are the same, set the exponents equal: \( 5x = 4 \). Solving for \( x \) gives \( x = \frac{4}{5} \). To double-check, substitute \( x \) back into the original equation. \( 3125^{\frac{4}{5}} \) simplifies to \( (5^5)^{\frac{4}{5}} \), which equals \( 5^4 \), confirming that both sides are equal. So, the solution is \( x = \frac{4}{5} \).