1. Logarithmic Functions Section 2

2. Objectives Change Exponential Expressions to Logarithmic Expressions and Logarithmic Expressions to Exponential Expressions Evaluate Logarithmic Expressions Determine the Domain of a Logarithmic Function Graph Logarithmic Functions Solve Logarithmic Equations

3. where a > 0 and a ≠ 1 Domain: x > 0

4. Change to an equivalent logarithmic function

5. Change to an equivalent exponential function

6. Find the exact value of the logarithmic expression

7. Since logarithmic and exponential functions are inverses of each other, Domain of the logarithmic fx. = Range of the exponential fx. = (0, ∞) Range of the logarithmic fx. = Domain of the exponential fx. = (-∞, ∞) The argument of a logarithmic function must be greater than zero

8. Find the domain of the logarithmic function

9. Properties of the Logarithmic Function f(x) = log a x Domain: Positive reals Range: All reals x-intercept: 1 y-intercept: None y-axis is a vertical asymptote Decreasing if 0 1 Graph contains the points (1, 0), (a, 1), and (1/a, -1) Graph is smooth and continuous, with no corners or gaps

10. y = ln x if and only if x = e y (inverse functions) ======================== y = log x if and only if x = 10 y (inverse functions)

11. Solve the logarithmic equation.

13. Use a logarithm to solve the equation.

14. Pages 515-516 (22-56 even) ======================== Pages 517-518 (76-110 even, 118, 121)