# How do you rewrite log_2.6x as a ratio of common logs and natural logs?

Jul 21, 2017

Expressing ratio of common logs

${\log}_{2.6} x$

$= {\log}_{2.6} 10 \times {\log}_{10} x$

$= {\log}_{10} \frac{x}{\log} _ 102.6$

Expressing ratio of natural logs

${\log}_{2.6} x$

$= {\log}_{2.6} e \times {\log}_{e} x$

$= {\log}_{e} \frac{x}{\log} _ e 2.6$