Expand menu menu_open Minimize Start chapters Home History history History expand_more
{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
No results
{{ searchError }}
search
menu_open
{{ courseTrack.displayTitle }}
{{ statistics.percent }}% Sign in to view progress
{{ printedBook.courseTrack.name }} {{ printedBook.name }}
search Use offline Tools apps
Login account_circle menu_open

Evaluating Logarithms

Evaluating Logarithms 1.8 - Solution

arrow_back Return to Evaluating Logarithms

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 yy is the exponent to which bb must be raised to get x.x. In our exercise, 44 is the exponent to which 55 must be raised to get 625.625. log5(625)=4625=54\begin{gathered} \log_{{\color{#0000FF}{5}}}({\color{#FF0000}{625}})=\textcolor{darkviolet}{4} \quad \Leftrightarrow \quad {\color{#FF0000}{625}}={\color{#0000FF}{5}}^{\textcolor{darkviolet}{4}} \end{gathered}