# How do you express log_50 23 in common logarithms?

Oct 31, 2016

${\log}_{50} \left(23\right) = {\log}_{10} \frac{23}{\log} _ 10 \left(50\right) = \ln \frac{23}{\ln} \left(50\right)$

#### Explanation:

Use the identity ${\log}_{c} \left(a\right) = {\log}_{b} \frac{a}{\log} _ b \left(c\right)$

The logarithms commonly found on calculators are base 10, ${\log}_{10}$, and base e, $\ln$

${\log}_{50} \left(23\right) = {\log}_{10} \frac{23}{\log} _ 10 \left(50\right) = \ln \frac{23}{\ln} \left(50\right)$