How do you evaluate $log_2 (1/4)$ ?

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Answer 1 · 2016-08-17T17:49:01

To understand logs, read $log_2 (1/4)$ as asking the question..

"What index of 2 will give $1/4$ "?

Write $1/4$ in a different form. $rarr " "1/4 = 1/2^2 = 2^(-2)$

"What index of 2 will give $2^(-2)$ ?

The answer is obviously -2.

$:. log_2 (1/4) = -2$

Or convert $log_2 (1/4)$ to index form.

$log_2 (1/4) = x " "rArr 2^x = 1/4$

Solve the exponential equation by making the bases the same.

$2^x = 1/4 = 1/2^2 = 2^-2$

If $2^x = 2^-2$

$x = -2$

How do you evaluate log_2 (1/4)log_2 (1/4)?