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

Aug 17, 2016

To understand logs, read ${\log}_{2} \left(\frac{1}{4}\right)$ as asking the question..

"What index of 2 will give $\frac{1}{4}$"?

Write $\frac{1}{4}$ in a different form.$\rightarrow \text{ } \frac{1}{4} = \frac{1}{2} ^ 2 = {2}^{- 2}$

"What index of 2 will give ${2}^{- 2}$?

$\therefore {\log}_{2} \left(\frac{1}{4}\right) = - 2$

Or convert ${\log}_{2} \left(\frac{1}{4}\right)$ to index form.

${\log}_{2} \left(\frac{1}{4}\right) = x \text{ } \Rightarrow {2}^{x} = \frac{1}{4}$

Solve the exponential equation by making the bases the same.

${2}^{x} = \frac{1}{4} = \frac{1}{2} ^ 2 = {2}^{-} 2$

If ${2}^{x} = {2}^{-} 2$

$x = - 2$