# What is log_(1/2) 4?

Sep 29, 2016

$- 2$

#### Explanation:

You can rewrite this question easily as

${\left(\frac{1}{2}\right)}^{x} = 4$

That is the purpose of a log: to find the value of the exponent. For this problem, we simply rewrite it and the do some math. Since

$\frac{1}{2} < 1 \text{ }$ and $\text{ } 4 > 1$

we know the exponent must be negative. That allows us to write the equation as

${2}^{- x} = 4$

So, $2$ to the power of what gets us $4$? The answer is $2$

${2}^{2} = 4$

Thus, you get $- 2$.