# How do you calculate log_6 (2)?

Apr 29, 2016

log 2/log 6 = 0.386853, nearly

#### Explanation:

Use ${\log}_{b} a = {\log}_{c} \frac{a}{\log} _ c b$, where c is at your choice.

Let us choose c as either 10 or e. Then

${\log}_{6} 2 = {\log}_{10} \frac{2}{\log} _ 10 6 = \ln \frac{2}{\ln} 6 = 0.386853$, nearly.

I am sure that this comparison, using different bases, would reinforce the formula used, in the long term memory.