2. Investigating Log Properties
What patterns do you notice?
logb u logb v logb uv
log 10 = log 100 = log 1000 =
log 0.1 = log 0.01 = log 0.001 =
log2 4 = log2 8 = log2 32 =
logb uv = logb u + logb v

3. Properties of Logs
 Product Property -
 Quotient Property –
 Power Property -

4. Using Properties of Logs
 Use log5 3 ≈ 0.683 and log5 7 ≈ 1.209 to
approximate:




5. Your Turn!
 Use log9 5 ≈ 0.732 and log9 11 ≈ 1.091 to
approximate:




6. Expanding Log Expressions
 Use properties of logs to expand.
 Example:

7. Condensing Log Expressions
 Use properties of logs to condense.
 Examples:
 log 6 + 2 log 2 – log 3
 2 log3 7 – 5 log3 x

8. Your Turn!
 Expand
 Condense

9. Change of Base Formula
 Allows us to write any logarithm in terms of
common or natural logs.
and

10. Evaluating Expressions
 Evaluate log3 7 using common and natural
logs.

11. Your Turn!
 Evaluate log6 15 using natural logarithms.