# How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_2 6 +log_3 5?

Nov 3, 2015

I found $\approx 4.05$

#### Explanation:

The Change of Base Formula allows you to change the base of your log to a more "friendly" base such as $e$ or $10$ that can be evaluated using a pocket calculator:
${\log}_{b} x = {\log}_{c} \frac{x}{\log} _ c b$ from base $b$ to $c$;
In our case we can use, say, $e$ as new base to get Natural Logs as:
${\log}_{2} \left(6\right) + {\log}_{3} \left(5\right) = \ln \frac{6}{\ln} 2 + \ln \frac{5}{\ln} 3 =$
using a pocket calculator you get:
$= \frac{1.79175}{0.69314} + \frac{1.60943}{1.09861} \approx 4.05$