Question

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

Answer 1

`x = log66/log4`

Using a calculator gives `x = 3.022`

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 `log_4 66= x " then " 4^x = 66`

Let's use the index form and find the log of both sides, because the variable is in the index.
`log4^x = log 66`

`xlog 4 = log66`

`x = log66/log4`

Using a calculator gives `x = 3.022`

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

`log_a b = log_10 b/log_10 a`

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