How do you evaluate ${log}_{\frac{1}{4}} (\frac{1}{64})$ $log_(1/4)( 1/64)$ ?

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Answer 1 · 2016-09-11T18:18:24

${log}_{\frac{1}{4}} (\frac{1}{64}) = 3$ $log_(1/4) (1/64) = 3$

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

"To what power/index must $\frac{1}{4}$ $1/4$ be raised to give $\frac{1}{64}$ $1/64$ ?"

OR: "How can I make $\frac{1}{4}$ $1/4$ into $\frac{1}{64}$ $1/64$ 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 $10^3 =1,000$

How do you evaluate log_(1/4)( 1/64)log14(164)log_(1/4)( 1/64)?