# How do you calculate log_9 48 with a calculator?

Dec 10, 2017

Use the change of base formula with $\log$ or $\ln$ ...

#### Explanation:

You can use the change of base formula for logarithms:

${\log}_{b} a = {\log}_{c} \frac{a}{\log} _ c b$

with $c = 10$ (common logarithm) or $c = e$ (natural logarithm):

${\log}_{9} 48 = \log \frac{48}{\log} 9 \approx \frac{1.681241237}{0.954242509} \approx 1.761859507$

${\log}_{9} 48 = \ln \frac{48}{\ln} 9 \approx \frac{3.871291911}{2.197224577} \approx 1.761859507$