# How do you write 64=4^x in Logarithm form?

Sep 1, 2016

${\log}_{4} 64 = x$

#### Explanation:

(this follows from the basic definition of log)

Sep 1, 2016

${\log}_{\textcolor{red}{a}} \textcolor{b l u e}{b} = \textcolor{\lim e}{c} \Leftrightarrow {\textcolor{red}{a}}^{\textcolor{\lim e}{c}} = \textcolor{b l u e}{b}$

${\log}_{\textcolor{red}{4}} \textcolor{b l u e}{64} = \textcolor{\lim e}{x} \Leftrightarrow {\textcolor{red}{4}}^{\textcolor{\lim e}{x}} = \textcolor{b l u e}{64}$

"The $\textcolor{red}{\text{base}}$ stays the $\textcolor{red}{\text{base}}$, and the other two change around"

#### Explanation:

log form and index form are interchangeable:

By definition: ${\log}_{\textcolor{red}{a}} \textcolor{b l u e}{b} = \textcolor{\lim e}{c} \Leftrightarrow {\textcolor{red}{a}}^{\textcolor{\lim e}{c}} = \textcolor{b l u e}{b}$

Remember the following:

"The $\textcolor{red}{\text{base}}$ stays the $\textcolor{red}{\text{base}}$, and the other two change around"

${\log}_{\textcolor{red}{4}} \textcolor{b l u e}{64} = \textcolor{\lim e}{x} \Leftrightarrow {\textcolor{red}{4}}^{\textcolor{\lim e}{x}} = \textcolor{b l u e}{64}$

${\log}_{\textcolor{red}{4}} \textcolor{b l u e}{64} = \textcolor{\lim e}{3} \Leftrightarrow {\textcolor{red}{4}}^{\textcolor{\lim e}{3}} = \textcolor{b l u e}{64}$