# How do you calculate log _10 (2)?

Mar 10, 2018

${\log}_{10} \left(2\right) \approx 0.301$

#### Explanation:

Whenever we have a log problem like this, we can simplify using the Change of Base Property/Formula that states

${\log}_{a} \left(b\right) = \left({\log}_{10} \frac{b}{\log} _ 10 \left(a\right)\right)$

Which is also equal to

${\log}_{a} \left(b\right) = \ln \frac{b}{\ln} \left(a\right)$, where $\ln =$natural log

In our case, our base ($a$) is equal to $10$, and our $b$ is $2$. Using the Change of Base Property, ${\log}_{10} \left(2\right)$ is equal to:

$= {\log}_{10} \frac{2}{{\log}_{10} \left(10\right)}$

$\implies \ln \frac{2}{\ln} 10$ (Which is the same thing as ${\log}_{10} \left(2\right)$)

Which, through evaluating with a calculator, we get:

${\log}_{10} \left(2\right) \approx 0.301$