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Section 1.8 : Logarithm Functions
2. Without using a calculator determine the exact value of \({\log _5}125\).
Hint : Recall that converting a logarithm to exponential form can often help to evaluate these kinds of logarithms.
Converting the logarithm to exponential form gives,
\[{\log _5}125 = ?\hspace{0.25in}\hspace{0.25in} \Rightarrow \hspace{0.25in}\hspace{0.25in}{5^?} = 125\]From this we can quickly see that \({5^3} = 125\) and so we must have,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{{{\log }_5}125 = 3}}\]