Logarithms

Introduction to Logarithms

In its simplest form, a logarithm answers the question:

 How many of one number do we multiply to get another number?

Example 1:  

log₂(8)

How many 2 do we multiply to get 8? 

2 × 2 × 2 = 8, so we needed to multiply 3 of the 2 to get 8

logarithm = 3

Answer: log₂(8) = 3

The same as:

The number we are multiplying is called the "base", so we can say:

• "the logarithm of 8 with base 2 is 3"
• or "log base 2 of 8 is 3"
• or "the base-2 log of 8 is 3"

Example 2:

 log₅(625)

5 × 5 × 5 × 5 = 625

Answer: log₅(625) = 4

 

Exponent

The exponent says how many times to use the number in a multiplication.

In this example: 2³ = 2 × 2 × 2 = 8

(2 is used 3 times in a multiplication to get 8)

 

The base is "2" and the exponent is "3"

Example 1: 


log₁₀(100)

10² = 100

So an exponent of 2 is needed to make 10 into 100

Answer: log₁₀(100) = 2

Example 2: 

log₃(81)

3⁴ = 81

So an exponent of 4 is needed to make 3 into 81, and:
Answer: log₃(81) = 4

 Now, Let's try some exercises!

References:
https://www.mathsisfun.com/algebra/logarithms.html