Question

How do you evaluate `log_(1/4)( 1/64)`?

Answer 1

`log_(1/4) (1/64) = 3`

Explanation:

In log format like this one, the question being asked is

"To what power/index must `1/4` be raised to give `1/64`?"

OR: "How can I make `1/4` into `1/64` using an index?"

`4^3 =64, :. (1/4)^3 = 1/64`

Clearly the answer is 3.

`log_(1/4) (1/64) = 3`

OR `rarr`Log form and index form are interchangeable:

`log_a b= c " " hArr" " a^c=b`

`log_(1/4) (1/64) = x" " hArr " " (1/4)^x = 1/64`

`x=3`

It will be a distinct advantage in your work with logs and indices if you know all the powers of the numbers from 1 to 10 (up to 1,000) by heart.

Ie up to `10^3 =1,000`