How do you solve 6^x=216?

1 Answer
Oct 13, 2016

x=3

Explanation:

You can decompose 216 to see its prime factors:

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

Thus, 2016 = 2^3 * 3^3

But this means that 2016 = (2*3)^3=6^3, and thus x=3