Change of Base Formula

Calculators only have buttons for $log_{10}$ , written log, and $log_e$ , written ln.

So how can we take $log_2$ using our calculators? If it’s hard we need to use our calculators!

We use the Change of Base Formula!!!

$log_{b}(a)=\frac{log_{c}(b)}{log_{c}(a)}$

Example 1: $log_6(7776)=\frac{log(7776)}{log(6)}=5$

Given

$log_{a}(x)=y \Longleftrightarrow a^y=x$

Want to find

$log_{b}(x)$

Since

$x=a^y \Longrightarrow log_{b}(x)=log_{b}(a^y)$

Power property

$log_{b}(x)=ylog_{b}(a)$

Solving

$y=\frac{log_{b}(x)}{log_{b}(a)}$

Wolf Math