# How do you calculate #log_6 5# with a calculator?

##### 1 Answer

Aug 12, 2016

#### Answer:

#### Explanation:

Use the change of base formula:

#log_a b = (log_c b) / (log_c a)#

So you can use natural or common logs:

#log_6 5 = ln 5 / ln 6#

#log_6 5 = log 5 / log 6#

In fact, if you know

#log_6 5 = log 5 / log 6 = (log 10 - log 2) / (log 2 + log 3)#

#~~ (1-0.30103)/(0.30103+0.47712) = 0.69897/0.77815 ~~ 0.89825#

Actually the true value is closer to