# How do you solve  2^x = 20?

Feb 29, 2016

Use basic properties of logarithms to remove $x$ from the exponent to find that

$x = {\log}_{2} \left(20\right) \approx 4.322$

#### Explanation:

We will use the following properties of logarithms:

• $\log \left({a}^{x}\right) = x \log \left(a\right)$
• ${\log}_{a} \left(a\right) = 1$

With these, we have

${2}^{x} = 20$

$\implies {\log}_{2} \left({2}^{x}\right) = {\log}_{2} \left(20\right)$

$\implies x {\log}_{2} \left(2\right) = {\log}_{2} \left(20\right)$

$\implies x \left(1\right) = {\log}_{2} \left(20\right)$

$\therefore x = {\log}_{2} \left(20\right) \approx 4.322$