1. Section 5.3 Properties of Logarithms Advanced Algebra

2. Properties of Logarithms log b 1 = 0 Anything raised to the 0 power is 1. log b b = 1 Anything raised to the 1st power is that anything log b b x = x Think about as exponent: b x = b x Rewrite as a log: log b x = log b x

3. Common and Natural Log Properties log 1 = 0 log 10 = 1 log 10 x = x 10 log x = x x > 0 ln 1 = 0 ln e = 1 ln e x = x e ln x = x if x > 0

4. Simplifying

5. Simplify Using Properties

6. More Simplifying

9. 3 More Properties Product Rule log b MN = log b M + log b N Quotient Rule Power Rule

10. Write as a sum or difference of logs

11. Expand as a sum and difference of logs

12. Expand the log into a sum or difference of logs

13. Write the difference as a single log

14. Write the sum as a single log To use the product or quotient rules of logs, remember, the bases must be the same.

15. Combine into a single log

16. Condense to a single logarithm

17. Evaluate log 4 5 Change of Base Formula

18. Evaluate