# How do you evaluate #Log_sqrt3 243 #?

##### 1 Answer

Mar 13, 2016

#### Answer:

#### Explanation:

We should try to write

An example of the method we should attempt can be shown more easily in evaluating

#log_2 8=log_2 2^3=3log_2 2=3#

The first step we should take for

#log_sqrt3 243=log_sqrt3 3^5#

But we still haven't addressed the issue that we want a base of

We should use the fact that

#log_sqrt3 3^5=log_sqrt3 ((sqrt3)^2)^5#

Using the rule that

#log_sqrt3 ((sqrt3)^2)^5=log_sqrt3 (sqrt3)^10#

Now, simplify as was done earlier.

#log_sqrt3 (sqrt3)^10=10log_sqrt3sqrt3=10#