1. Unit 5: Properties of Logarithms MEMORIZE THEM!!! Exponential Reasoning [1] [2] [3] [4] Cannot take logs of negative number [3b]

2. Useful Log Properties: Examples [1] [2] [3] [5]

3. Base – Base (Inverse property: True for all logs that have same base of log as base of power) a) b) c) d) e) f) g) h) i)

4. OPERATION PROPERTIES OF LOGARITHMS #1) Product Property: #2) Quotient Property: #3) Power Property: Log of a product is equal to the SUM of the logs of both multipliers of the same base Log of a quotient “fraction” is equal to the DIFFERENCE of the logs of the numerator and denominator Log of a power statement is equal to the MULTIPLICATION of the power (p) times the log of the power’s base (m)

5. OPERATION PROPERTIES OF LOGARITHMS Condense:Expand (1a) (2a) (1b) (3a) (2b) (3b)

6. Expand Each Logarithm Using Properties (1) (7) (3) (5) (2) (6) (4) (8) (9)

7. Condense Each Logarithm Using Properties (1) (4) (5) (2) (6) (3)

8. Log Property Practice Condense each Log Expression 1. 2. 3.

9. NATURAL LOG PROPERTIES: All Log Properties work for Natural Logs because its just a special notation for base e a) b) c) d)

10. Evaluating Log Expressions: General Rules 1)Set the log expression equal to x 2)Convert log to exponential form 3)Solve the resulting exponential equation for x. “2 raised to what power equals 8?”

11. Example 2Evaluate using properties (algebraic proof) a) c) e) b) d) f)

12. Use the given values and log properties to evaluate 4.6. 5. 7. 8.