# How do you evaluate #log_(4) 66 #?

##### 1 Answer

Jun 12, 2016

#### Answer:

Using a calculator gives

#### Explanation:

The answer is not going to be an integer. The question is asking:

"To what power must 4 be raised, to equal 66?"

The powers of 4 are : 4, 16, 64, 256 ....

66 is not one of them, but we can see that the required index will be 3. .....

log from is interchangeable with index form:

If

Let's use the index form and find the log of both sides, because the variable is in the index.

Using a calculator gives

This same result could be found from the change of base law:

Some calculators can work with any base, but for those that only use base 10, this works fine.1