# How do you find the value of log_7 4 using the change of base formula?

Nov 1, 2016

$0.715$

#### Explanation:

You can use the change of base formula to be able to use ${\log}_{10}$

${\log}_{7} 4 = \frac{{\log}_{10} 4}{{\log}_{10} 7}$

This is now calculated with a calculator:

$= 0.715$

The follow explains where the rule comes from...

${\log}_{7} 4 = x \text{ "hArr" " 7^x = 4} \leftarrow$ log both sides

$\textcolor{w h i t e}{\times \times \times \times \times \times \times} \log {7}^{x} = \log 4 \text{ } \leftarrow$ power law

$\textcolor{w h i t e}{\times \times \times \times \times . \times x} x \log 7 = \log 4 \text{ } \leftarrow$ isolate x

$\textcolor{w h i t e}{\times \times \times \times \times \times \times \times x} x = \log \frac{4}{\log} 7$