# How do you evaluate #log_3 64#?

##### 2 Answers

Dec 26, 2016

I found

#### Explanation:

I would try to change base and use a pocket calculator. The natural log,

Remember that to change base to a new base

Dec 26, 2016

#### Explanation:

Suppose you know the following approximations:

#log_10 2 ~~ 0.30103#

#log_10 3 ~~ 0.47712125#

The change of base formula tells us that:

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

for any

So we find:

#log_3 64 = (log_10 64)/(log_10 3) = (log_10 2^6)/(log_10 3) = (6 log_10 2)/(log_10 3) ~~ (6*0.30103)/(0.47712125) ~~ 3.7855786#