# How do you solve 2^x=0.5?

Mar 10, 2018

$x = - 1$

#### Explanation:

We know that for any ${a}^{x} = b$, ${\log}_{a} b = x$

Here, $a = 2$ and $b = 0.5$. So we take:

${\log}_{2} 0.5 = - 1$

So $x = - 1$

Mar 10, 2018

The answer is $x = - 1$.

#### Explanation:

Rewrite $0.5$ as $\frac{1}{2}$, then make the exponents equal each other.

${2}^{x} = 0.5$

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

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

${2}^{x} = {2}^{-} 1$

${2}^{\textcolor{red}{x}} = {2}^{\textcolor{red}{- 1}}$

$x = - 1$