# Is the graph of log(1/2)^x always decreasing?

Sep 20, 2016

This function is decreasing.

#### Explanation:

To find if the function is incresing, decreasing or constant you have to simplify it first.

## $y = \log {\left(\frac{1}{2}\right)}^{x}$

$y = \log {\left(\frac{1}{2}\right)}^{x} = x \times \log \left(\frac{1}{2}\right)$

From this form we see that the function is linear and its slope is $\log \left(\frac{1}{2}\right)$. This number is negative, so the function is decreasing in all domain $\mathbb{R}$