Section 6.2 : Logarithm Functions
7. Without using a calculator determine the exact value of \({\log _3}81\).
Show All Steps Hide All Steps
Hint : Recall that converting a logarithm to exponential form can often help to evaluate these kinds of logarithms.
Start Solution
Converting the logarithm to exponential form gives,
\[{\log _3}81 = ?\hspace{0.25in} \Rightarrow \hspace{0.25in}{3^?} = 81\]Show Step 2
From this we can quickly see that \({3^4} = 81\) and so we must have,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{{{\log }_3}81 = 4}}\]