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Evaluating Logarithms

Evaluating Logarithms 1.2 - Solution

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To write the given equation in exponential form, we will recall the definition of a logarithm. logb(x)=yx=by\begin{gathered} \log_{{\color{#0000FF}{b}}}({\color{#FF0000}{x}})=\textcolor{darkviolet}{y} \quad \Leftrightarrow \quad {\color{#FF0000}{x}}={\color{#0000FF}{b}}^{\textcolor{darkviolet}{y}} \end{gathered} This means that y\textcolor{darkviolet}{y} is the exponent to which b{\color{#0000FF}{b}} must be raised to get x.{\color{#FF0000}{x}}. In our exercise, 3\textcolor{darkviolet}{3} is the exponent to which 7{\color{#0000FF}{7}} must be raised to get 343.{\color{#FF0000}{343}}. log7(343)=3343=73\begin{gathered} \log_{{\color{#0000FF}{7}}}({\color{#FF0000}{343}})=\textcolor{darkviolet}{3} \quad \Leftrightarrow \quad {\color{#FF0000}{343}}={\color{#0000FF}{7}}^{\textcolor{darkviolet}{3}} \end{gathered}