# How do you evaluate log_4 (8)?

May 7, 2018

$1.5$

#### Explanation:

Since ${4}^{1} = 4$ and ${4}^{2} = 16$, the answer lies between $1$ and $2$. There is no much more that we can do by hands, so I'm assuming you meant something like "how to compute ${\log}_{4} \left(8\right)$ with a calulator?"

If so, you must use the rule that allows us to change the base:

${\log}_{a} \left(b\right) = {\log}_{c} \frac{b}{\log} _ c \left(a\right)$

So, assuming your calculator has a button for the natural logarithm, you have

${\log}_{4} \left(8\right) = \setminus \frac{\ln \left(8\right)}{\ln \left(4\right)} = 1.5$