1. Unit 5: Logarithmic Functions
Inverse of exponential functions.
Domain:
Range:
Domain:
Range:
Ex 1:
Ex 2:

2. Logarithmic and Exponential Conversions
(1) Base is always the base (2) Exponent and Answer switch
Convert each log expression into an exponential expression. 1. 2. 3.
Convert each exponential expression into a log expression. 4. 5. 6.

3. Example 1 CONVERSION PRACTICE Exponential Logarithmic
b) __________________
c) ______________
d) ______________
f) __________________
f) ______________

4. Example 1: Continued (Fill In The Blanks)
Exponential Logarithmic
a) __________________
b) ______________
c) __________________
d) ______________
f) __________________
f) ______________

5. Useful Log Properties: MEMORIZE THEM!!!
Exponential Reasoning
[1]
[2]
[3]
[4] Cannot take logs of negative number
[5] “change of base formula”
(for calculator)

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

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

8. OPERATION PROPERTIES OF LOGARITHMS
EXAMPLES
(1a)
(1b)
(2a)
(2b)
(3a)
(3b)

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

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

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

12. Example 2 Evaluate using properties (algebraic proof)d) e) f)

13. Solve Exponential Equations with Logs
Solve the exponential until form, bx = a.
Clearing Bases Using Log Conversion
Some answers cannot be evaluated by hand and require calculator b) a)

14. Solving LOG Equations and Inequalities
**SIMPLIFY all LOG Expressions**
CASE #1: LOG on one side and VALUE on other Side
Apply Exponential Conversion
Solve (For inequalities x < # requires 0 < x < # because of domain b) a) c) d)

15. Solving LOG Equations and Inequalities
**Simplify all LOG Expressions**
CASE #2: LOG on BOTH
Bases of both sides should be the same
Set the insides of logs equal and Solve a) b) c)

16. Practice: Solving Logs2. 1. 3. 4. 5.

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

18. Use the given values and log properties to evaluate4. 5. 6. 7. 8. 8.

19. APPLYING LOG PROPERTIES: SOLVING with PRODUCT PROPERTY
[b]

20. [c]
[d]

21. APPLYING LOG PROPERTIES: SOLVING with QUOTIENT PROPERTY
[b]

22. APPLYING LOG PROPERTIES: SOLVING with POWER PROPERTY
[b]
[a]

23. GENERAL PRACTICE
[a]
[b]
[c]
[d]

24. GENERAL PRACTICE: Continued
[f]