1. Logarithm Definition Example 1 : Write x in index form or as a number. If log a b = c then a c =b log 10 x = 3 then x=10 3 =1000 log x = 3 then x=10 3 =1000 a is called the “base”. If it is left out then a=10 This will be written without the 10 as follows:

2. Logarithm Definition Examples 2 : Write x in index form or as a number. If log a b = c then a c =b log x = 2 then x=10 2 =100 a is called the “base”. If it is left out then a=10

3. Logarithm Definition Example 3 : Write x in index form or as a number. If log a b = c then a c =b log 5 x = 2 then x=5 2 =25 a is called the “base”. If it is left out then a=10

4. Properties of Logarithms (base 10) Examples : Write as a single number. log A + log B = log AB log 5 + log 6 = log 5 ×6 = log 30 log 2 + log 8 = log 2 ×8 = log 16

5. Properties of Logarithms (base 10) Examples : Write as a single number. log A – log B = log A / B log 40 – log 8 = log 40 ÷8 = log 5 log 24 – log 6 = log 24 ÷6 = log 4

6. Properties of Logarithms (base 10) Examples : Write as a single number. log A r = r × log A 2log 4 = log 4 2 = log 16 3log 2 = log 2 3 = log 8

7. Properties of Logarithms (base 10) Examples : Write as a single number. log A r = r × log A ½ log 9 = log 9 ½ = log 9 = log 3

8. Properties of Logarithms (base 10) Examples : Write as a single number. log A + log B = log AB 2log 3 + log 5 = log 3 2 ×5 = log 45 3log 4 – log 2 = log 4 3 ×2 = log 32 log A – log B = log A / B log A r = r × log A