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

• A. $25^{\frac12}=5$
• B. $5^2=25$
• C. $2^5=25$
• D. $25^2=625$

Answer: (B)

Verified step by step guidance

1. Since the problem is titled 'Intro to Logarithms Practice 4', let's start by recalling the basic definition of a logarithm: for \(a > 0\), \(a \neq 1\), and \(x > 0\), the logarithm \(\log_a x = y\) means that \(a^y = x\).
2. Identify the base of the logarithm and the argument (the value inside the log). This will help in rewriting the logarithmic equation into its equivalent exponential form.
3. Use logarithm properties such as the product rule \(\log_a (xy) = \log_a x + \log_a y\), the quotient rule \(\log_a \left(\frac{x}{y}\right) = \log_a x - \log_a y\), and the power rule \(\log_a (x^r) = r \log_a x\) to simplify the expression if needed.
4. If the problem involves solving for a variable inside the logarithm, rewrite the logarithmic equation in exponential form and then solve the resulting equation algebraically.
5. Check your solution by substituting it back into the original logarithmic expression to ensure the argument of the logarithm is positive and the equation holds true.