# How do you evaluate log3^4?

Apr 30, 2016

$1.908$

#### Explanation:

A $\log$ tells you how many times you multiply the base by itself to get ${3}^{4}$, or whatever else you put inside it. The base here isn't made explicit, so I'm going to assume it's $10$, so

${\log}_{10} {3}^{4}$

According to the law of logarithms where $\log {a}^{n} = n \log a$,

${\log}_{10} {3}^{4} = 4 {\log}_{10} 3$,

you can now simply use a calculator to find

$4 {\log}_{10} 3 \approx 4 \left(0.477\right) = 1.908$

You can check this by doing

${10}^{1.908} = 80.9 \approx 81 = {3}^{4}$