Rewrite the logarithmic equation as an exponential equation.
${\log }_5\left(25\right)=2$

• A. ${25}^{\frac{1}{2}}=5$
• B. $5^2=25$
• C. $2^5=25$
• D. ${25}^2=625$

Answer: (B)

Verified step by step guidance

1. Recall the definition of a logarithm: if \(\log_b(a) = c\), then the equivalent exponential form is \(b^c = a\).
2. Identify the base \(b\), the result \(a\), and the logarithm value \(c\) from the given equation \(\log_5(25) = 2\).
3. Here, the base \(b\) is 5, the logarithm value \(c\) is 2, and the result \(a\) is 25.
4. Rewrite the logarithmic equation as an exponential equation by raising the base to the power of the logarithm value: \$5^2 = 25$.
5. This shows the equivalence between the logarithmic and exponential forms.