# Given log_b 2= 0.3562, log_b 3=0.5646, and log_b 5=0.8271, how do you evaluate log_b15?

May 13, 2016

${\log}_{b} 15 = 1.3917$

#### Explanation:

To calculate ${\log}_{b} 15$ we use the formula ${\log}_{b} a \cdot c = {\log}_{b} a + {\log}_{b} c$

First we have to write $15$ as a product of numbers $2 , 3 \mathmr{and} 5$. Number $2$ will not be used because $15$ is an odd number, but we can write that $15 = 3 \cdot 5$

Now we can use the formula above to write the logarythm as a sum of 2 given values.

${\log}_{b} 15 = {\log}_{b} 3 \cdot 5 = {\log}_{b} 3 + {\log}_{b} 5 = 0.5646 + 0.8271 = 1.3917$