1. Properties of Logarithms Change of Base Formula:

2. The inverse function of an Exponential functions is a log function. The inverse function of an Exponential functions is a log function. Domain: Range: Key Points: Asymptotes: Graphing Logarithmic Functions

3. Section 4.5 Properties of Logarithms Condense and Expand Logarithmic Expressions.

4. Rewrite expression to get same base on each side of equal sign. where u and v are expressions in x where u and v are expressions in x Type 1. Solving Exponential Equations

5. Exponential Equations with base e Treat as a number. Rewrite these expressions to have a single base e on both sides of the equation

6. Type 2 Log = Log Type 2 Solving: Log = Log If then u = v When solving log functions, we must check that a solution lies in the domain!

7. Log ( ) = Constant Type 3. Solving: Log ( ) = Constant Isolate and rewrite as exponential

8. Exponential = Constant Type 4: Exponential = Constant Isolate exponential part and rewrite as log

9. 1. Power Rule “Expanding a logarithmic expression” Rewrite using the power rule. “Expanding a logarithmic expression” Rewrite using the power rule.

10. 2. Product Rule “Expanding a logarithmic expression” Rewrite using the Product Rule. “Expanding a logarithmic expression” Rewrite using the Product Rule.

11. 3. Quotient Rule “Expanding a logarithmic expression” Rewrite using the Quotient Rule. “Expanding a logarithmic expression” Rewrite using the Quotient Rule.

12. 4. Expand the following expressions completely

13. 5. Condensing Logarithmic Expressions Rewrite as a single log expression Coefficients of logarithms must be 1 before you can condense them.

14. More practice….

15. 7. Change-of-Base Formula Example. Find an approximation for