# How do you calculate log_9 1.1 with a calculator?

Apr 16, 2018

${\log}_{9} 1.1 = \ln \frac{1.1}{\ln} \left(9\right) \approx 0.043$
Recall that ${\log}_{a} b = {\log}_{c} \frac{b}{\log} _ c a = \ln \frac{b}{\ln} \left(a\right) .$
Here, we see $a = 9 , b = 1.1 ,$ so
${\log}_{9} 1.1 = \ln \frac{1.1}{\ln} \left(9\right) \approx 0.043$