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 = square 3x3 is 9 = 3 × 3 = 9

Using Exponents we write it as:

32 = 9

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

 

32 = ?

This is an exponent question, "What is 3 squared?":   32 = 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?":   log3(9) = 2

 

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

 

One more example:

103 = 1000

103 = ?

"What is 10 cubed?":   103 = 1000

 

?3 = 1000

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

 

10? = 1000

"What is log base 10 of 1000?":   log10(1000) = 3

 

Can you think of a better notation?