Questions: logp(625) = 4

Solution Steps

To convert a logarithmic equation to its exponential form, we use the definition of a logarithm: if \(\log_b(a) = c\), then the equivalent exponential form is \(b^c = a\). Applying this to the given equation \(\log_p(625) = 4\), we can rewrite it in exponential form as \(p^4 = 625\).

The given logarithmic equation is

\[ \log_{p}(625) = 4. \]

Using the definition of logarithms, we can convert this to its exponential form:

\[ p^4 = 625. \]

To find \( p \), we need to isolate it. We can do this by taking the fourth root of both sides:

\[ p = 625^{\frac{1}{4}}. \]

Next, we simplify \( 625^{\frac{1}{4}} \). Since \( 625 = 5^4 \), we have:

\[ p = (5^4)^{\frac{1}{4}} = 5. \]

Final Answer