# How do you solve 6^x=216?

Oct 13, 2016

$x = 3$

#### Explanation:

You can decompose $216$ to see its prime factors:

$216 \setminus \div 2 = 108$
$108 \setminus \div 2 = 54$
$54 \setminus \div 2 = 27$
$27 \setminus \div 3 = 9$
$9 \setminus \div 3 = 3$
$3 \setminus \div 3 = 1$

Thus, $2016 = {2}^{3} \cdot {3}^{3}$

But this means that $2016 = {\left(2 \cdot 3\right)}^{3} = {6}^{3}$, and thus $x = 3$