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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.
Show Solution

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,

$\require{bbox} \bbox[2pt,border:1px solid black]{{{{\log }_5}125 = 3}}$