# How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_3 15?

${\log}_{3} 15 = \ln \frac{15}{\ln} 3 = \log \frac{15}{\log} 3 \approx 2.465$
${\log}_{b} a = \ln \frac{a}{\ln} b = {\log}_{c} \frac{a}{\log} _ c b$ where $c$ is the new base of your choice.
With $a = 15$ and $b = 3$, we get that ${\log}_{3} 15 = \ln \frac{15}{\ln} 3 = \log \frac{15}{\log} 3$ ($\log x$ is the base 10 logarithm) and using a calculator, it is approximately 2.465. The reason why we normally use the natural logarithm or the base 10 logarithm is that most calculators are equipped with these functions.