# Exponents, Roots and Logarithms

Exponents, Roots (such as square roots, cube roots etc) and Logarithms are all related!

Let's use the simple example of 3x3=9:

3 Squared | = | = 3 × 3 = 9 |

Using Exponents we write it as:

3^{2} = 9

When any of those values are missing, we have a question. And (unfortunately!) a different notation:

3^{2} = ?

This is an exponent question, "What is 3 squared?": 3^{2} = 9

?^{2} = 9

This is a root question, "What is the square root of 9?": √9 = 3

3^{?} = 9

This is a logarithm question, "What is log base 3 of 9?": log_{3}(9) = 2

So when you are stuck trying to solve questions with logs, roots or exponents just remember this.

One more example:

10^{3} = 1000

10^{3} = ?

"What is 10 cubed?": 10^{3} = 1000

?^{3} = 1000

"What is the cube root of 1000?": ∛1000 = 10

10^{?} = 1000

"What is log base 10 of 1000?": log_{10}(1000) = 3

*Can you think of a better notation?*