# How do you simplify log_8 16 + log_8 256?

Jun 20, 2016

Giving approximate answer of $4.004$ to 3 decimal places as a value

Simplified form$\to {\log}_{8} \left(4128\right)$

#### Explanation:

The addition of logs represents multiplication of the source numbers

${\log}_{8} \left(16\right) + {\log}_{8} \left(256\right) \text{ " =" " log_8(16xx258)" "=" } {\log}_{8} \left(4128\right)$

Converting log base 8 to log base 10

${\log}_{10} \frac{4128}{\log} _ 10 \left(8\right) \approx 4.0037$

Giving approximate answer of $4.004$ to 3 decimal places