A. Evaluate log Evaluate Logarithms
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3 A. Evaluate log Evaluate Logarithms
4 Evaluate Logarithms B. Evaluate.
5 C. Evaluate. Evaluate Logarithms
6 D. Evaluate log Evaluate Logarithms
7 Evaluate. A. 4 B. 4 C. 2 D. 2
8
9 A. Evaluate log Apply Properties of Logarithms
10 B. Evaluate 22 log Apply Properties of Logarithms
11 Evaluate 7 log 7 4. A. 4 B. 7 C. 4 7 D. 7 4
12 See slide 8 it s the same thing! Just tailored to log (base 10)
13 Common Logarithms A. Evaluate log 10,000.
14 B. Evaluate 10 log 12. Common Logarithms
15 Common Logarithms C. Evaluate log 14. Use a calculator.
16 Common Logarithms D. Evaluate log ( 11). Trick question!
17 Evaluate log A. about 1.04 B. about 1.04 C. no real solution D. about 2.39
18 See slide 8 it s the same thing! Just tailored to log (base e)
19 A. Evaluate ln e 4.6. Natural Logarithms
20 Natural Logarithms B. Evaluate ln ( 1.2).
21 C. Evaluate e ln 4. Natural Logarithms
22 D. Evaluate ln 7. Natural Logarithms
23 Evaluate ln e 5.2. A. no real solution B. about C. about 1.65 D. 5.2
24 Part II Graphing Logarithms
25 Logarithmic and exponential functions are inverses
26 Graphs of Logarithmic Functions A. Sketch and analyze the graph of f (x) = log 2 x. Describe its domain, range, intercepts, asymptotes, end behavior, and where the function is increasing or decreasing. Construct a table of values and graph the inverse of this logarithmic function, the exponential function f 1 (x) = 2 x.
27 Graphs of Logarithmic Functions Since f(x) = log 2 x and f 1 (x) = 2 x are inverses, you can obtain the graph of f(x) by plotting the points (f 1 (x), x).
28 Graphs of Logarithmic Functions
29 Graphs of Logarithmic Functions B. Sketch and analyze the graph of Describe its domain, range, intercepts, asymptotes, end behavior, and where the function is increasing or decreasing.
30 Graphs of Logarithmic Functions Since are inverses, you can obtain the graph of g(x) by plotting the points (g 1 (x), x).
31 Graphs of Logarithmic Functions
32 Describe the end behavior of f(x) = log 4 x. A. B. C. D.
33
34 Graph Transformations of Logarithmic Functions A. Use the graph of f(x) = log x to describe the transformation that results in p(x) = log (x + 1). Then sketch the graph of the function.
35 Graph Transformations of Logarithmic Functions B. Use the graph of f(x) = log x to describe the transformation that results in m(x) = log x 2. Then sketch the graph of the function.
36 Graph Transformations of Logarithmic Functions C. Use the graph of f(x) = log x to describe the transformation that results in n(x) = 5 log (x 3). Then sketch the graph of the function.
37 A. Use the graph of f(x) = ln x to describe the transformation that results in p(x) = ln (x 2) + 1. Then sketch the graphs of the functions. A. The graph of p(x) is the graph of f (x) translated 2 units to the left and 1 unit down. C. The graph of p(x) is the graph of f (x) translated 2 units to the left and 1 unit up. B. The graph of p(x) is the graph of f (x) translated 2 units to the right and 1 unit down. D. The graph of p(x) is the graph of f (x) translated 2 units to the right and 1 unit up.
38 Use Logarithmic Functions A. EARTHQUAKES The Richter scale measures the intensity R of an earthquake. The Richter scale uses the formula, where a is the amplitude (in microns) of the vertical ground motion, T is the period of the seismic wave in seconds, and B is a factor that accounts for the weakening of seismic waves. Find the intensity of an earthquake with an amplitude of 250 microns, a period of 2.1 seconds, and B = 5.4.
39 Use Logarithmic Functions R = Original Equation = a = 250, T = 2.1, and B = The intensity of the earthquake is about 7.5. Answer: about 7.5
40 Use Logarithmic Functions B. EARTHQUAKES The Richter scale measures the intensity R of an earthquake. The Richter scale uses the formula, where a is the amplitude (in microns) of the vertical ground motion, T is the period of the seismic wave in seconds, and B is a factor that accounts for the weakening of seismic waves. A city is not concerned about earthquakes with an intensity of less than 3.5. An earthquake occurs with an amplitude of 125 microns, a period of 0.33 seconds, and B = 1.2. What is the intensity of the earthquake? Should this earthquake be a concern for the city?
41 Use Logarithmic Functions R = Original Equation = a = 125, T = 0.33, and B = The intensity of the earthquake is about Since , the city should be concerned. Answer: about 3.78
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