# If log base 10 (2) = 0.301 & log base 10 (3) = 0.477, what does log base 10 (15) =?

Jan 28, 2016

I found: $1.176$

#### Explanation:

We can write it as:
${\log}_{10} \left(15\right) = {\log}_{10} \left(\frac{30}{2}\right)$
using the property of logs of a fraction we get:
${\log}_{10} \left(\frac{30}{2}\right) = {\log}_{10} \left(30\right) - {\log}_{10} \left(2\right) =$
and:
$= {\log}_{10} \left(10 \cdot 3\right) - {\log}_{10} \left(2\right) =$
we use the property of the log of a product to get:
${\log}_{10} \left(10\right) + {\log}_{10} \left(3\right) - {\log}_{10} \left(2\right) =$
$= 1 + 0.477 - 0.301 = 1.176$