# How do you use the Change of Base Formula and a calculator to evaluate log_2 8?

Oct 19, 2015

You should get $3$:

#### Explanation:

Actually using the definition of log you get:
${\log}_{2} \left(8\right) = x$
${2}^{x} = 8$
${2}^{x} = {2}^{3}$
$x = 3$
or:

The Change of Base Formula tells you that:
${\log}_{a} b = {\log}_{c} \frac{b}{\log} _ c a$ where $a$ is the old and $c$ is the new base.
We can choose $c = 10$ that gives you a log that can easily be evaluated using a pocket calculator getting:
${\log}_{2} \left(8\right) = {\log}_{10} \frac{8}{\log} _ 10 \left(2\right) = 3$