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Section 1.8 : Logarithm Functions

1. Without using a calculator determine the exact value of \({\log _3}81\).

Hint : Recall that converting a logarithm to exponential form can often help to evaluate these kinds of logarithms.
Show Solution

Converting the logarithm to exponential form gives,

\[{\log _3}81 = ?\hspace{0.25in}\hspace{0.25in} \Rightarrow \hspace{0.25in}\hspace{0.25in}{3^?} = 81\]

From this we can quickly see that \({3^4} = 81\) and so we must have,

\[\require{bbox} \bbox[2pt,border:1px solid black]{{{{\log }_3}81 = 4}}\]