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Logarithmic Functions

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Presentation on theme: "Logarithmic Functions"— Presentation transcript:

1 Logarithmic Functions
Objectives: Determine the domain of a Logarithmic function Graph Logarithmic Functions Solve Logarithmic Equations

2 Characteristics of the Graphs of Logarithmic Functions of the form
1. Domain: and Range: 2. The x-intercept is 1. There is no y-intercept 3. The y-axis, or , is the vertical asymptote 4. If , the function is increasing. If , the function is decreasing. 5. The graph passes through the points 6. The graph is smooth and continuous. It has no sharp corners or gaps.

3 EX: Graph each function
EX: Graph each function. Determine the domain, range and vertical asymptote of each function 1. 2.

4 EX: Graph each function
EX: Graph each function. Determine the domain, range and vertical asymptote of each function 3. 4.

5 EX: Find the domain of each Logarithmic Function
5. 6.

6 EX: Solve each logarithmic equation
7. 8. 9.

7 EX: Solve each logarithmic equation
10. 11.

8 EX: ATMOSPHERIC PRESSURE:
EX: ATMOSPHERIC PRESSURE: The atmospheric pressure p on a balloon or an aircraft decreases with increasing height. This pressure, measured in millimeter of mercury, is related to the height h (in kilometers) above sea level by the formula Find the height of an aircraft if the atmospheric pressure is 320 millimeters of mercury.

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