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

1 Answer
Sep 11, 2016

#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#