# How do you solve Log_2 32 = x?

Mar 9, 2016

$x = 5$

#### Explanation:

The logarithmic expression can be exponentiated with a base of $2$:

${2}^{{\log}_{2} 32} = {2}^{x}$

The ${2}^{x}$ and ${\log}_{2} x$ functions are inverses, which means that they undo one another, so we obtain the equation:

$32 = {2}^{x}$

We can write $32$ as a power of $2$:

${2}^{5} = {2}^{x}$

Since the bases are equal, we know their powers are also equal, giving:

$x = 5$

Mar 9, 2016

$x = 5$

#### Explanation:

Since $32 = {2}^{5}$, we see that

${\log}_{2} {2}^{5} = x$

Using the logarithm rule:

$\log \left({a}^{b}\right) = b \cdot \log \left(a\right)$

Giving the equation:

$5 \cdot {\log}_{2} 2 = x$

Since ${\log}_{a} a = 1$,

$x = 5$