# Exponents, Roots and Logarithms

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

Let's start with the simple example of **3 × 3 = 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, each with a **different notation**:

3

^{2}= ?is the exponent question "what is 3 squared?": 3^{2} = 9

?

^{2}= 9is the root question "what is the square root of 9?": √9 = 3

3

^{?}= 9is the logarithm question "what is log base 3 of 9?": log_{3}(9) = 2

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

Another 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