1. Section 11-4 Logarithmic Functions Objective: Students will be able to 1.Evaluate expressions involving logarithms 2.Solve equations involving logarithms 3.Graph logarithmic functions and inequalities

2. Example 1: Write each equation in exponential form. Since the graphs of exponential functions pass the horizontal line test, we know their inverses are also functions. Remember to find the inverse of a graph, we can switch the x & y variables around and then graph them. Inverse The graphs are reflections of each other across the line y = x.

3. Example 2: Write each equation in logarithmic form. x = -3 x = 5

4. Sum of Logs Difference of Logs Constant times a Log Equality To Solve Log Equations: Type 1: Logs on both sidesType 2: Logs on one side 1. 2.3.4. Properties of Logs Simplify on both sides to get one log on each side. (Use Prop. Of Logs.) Use Prop. Of Equality and drop the logs. Solve for the variable. Check your answers. Simplify to get only one log in the problem. Rewrite problem as an exponent. Solve for the variable. Check your answers.

5. Example 4: Solve each equation. c. log 8 (x + 1) + log 8 (x + 3) = log 8 24d. log 3 3x = -1 P = 81 5x – 3 = 10x + 2 -3 = 5x + 2 -5 = 5x -1 = x (x + 7)(x – 3) = 0 x = -7, 3 3

6. e. log 10 4 + 2 log 10 x = 2f. log 3 (x + 3) – log 3 (2x – 1) = log 3 2 To Graph Log Functions…. 1) 2) 3) 4) Rewrite the logarithm as an exponential Make an xy-table of values for the parent function. Pick numbers for y and solve for x. Shift the parent function based on a, b, h, and k. State the V.A., Domain and Range.

7. Example 5: Graph y = log 4 (x + 2). Example 6: Graph y = log 3 x - 4. h = -2 D: x > -2 R: R V.A. : x = -2 k = -4 D : x > 0 R : R V.A. : x = 0

8. Example 7: h = -1 k = -3 D: x > -1 R: R V.A.: x = -1

9. Example 8: Graph the following logarithmic inequality.c inequality Horizontal translation 1 lt.