Concept. Example 1 Logarithmic to Exponential Form A. Write log 3 9 = 2 in exponential form. Answer: 9 = 3 2 log 3 9 = 2 → 9 = 3 2.

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Presentation transcript:

Concept

Example 1 Logarithmic to Exponential Form A. Write log 3 9 = 2 in exponential form. Answer: 9 = 3 2 log 3 9 = 2 → 9 = 3 2

Example 1 Logarithmic to Exponential Form Answer: B. Write in exponential form.

Example 1 A.8 3 = 2 B.2 3 = 8 C.3 2 = 8 D.2 8 = 3 A. What is log 2 8 = 3 written in exponential form?

Example 1 B. What is –2 written in exponential form? A. B. C. D.

Example 2 Exponential to Logarithmic Form A. Write 5 3 = 125 in logarithmic form. Answer: log = = 125 → log = 3

Example 2 Exponential to Logarithmic Form B. Write in logarithmic form. Answer:

Example 2 A.log 3 81 = 4 B.log 4 81 = 3 C.log 81 3 = 4 D.log 3 4 = 81 A. What is 3 4 = 81 written in logarithmic form?

Example 2 B. What is written in logarithmic form? A. B. C. D.

Example 3 Evaluate Logarithmic Expressions Evaluate log log 3 243= yLet the logarithm equal y. 243= 3 y Definition of logarithm 3 5 = 3 y 243 = 3 5 5= yProperty of Equality for Exponential Functions Answer: So, log = 5.

Example 3 Evaluate log A. B.3 C.30 D.10,000

Concept

Example 4 Graph Logarithmic Functions A. Graph the function f(x) = log 3 x. Step 1Identify the base. b = 3 Step 2Determine points on the graph. Step 3Plot the points and sketch the graph. Because 3 > 1, use the points (1, 0), and (b, 1).

Example 4 Graph Logarithmic Functions (1, 0) (b, 1) → (3, 1) Answer:

Example 4 Graph Logarithmic Functions Step 1Identify the base. B. Graph the function Step 2Determine points on the graph.

Example 4 Graph Logarithmic Functions Step 3Sketch the graph. Answer:

Example 4 A. Graph the function f(x) = log 5 x. A. B. C.D.

Example 4 B. Graph the function. A. B. C.D.

Example 5 Graph Logarithmic Functions This represents a transformation of the graph f(x) = log 6 x. ● : The graph is compressed vertically. ● h = 0: There is no horizontal shift. ● k = –1: The graph is translated 1 unit down.

Example 5 Graph Logarithmic Functions Answer:

Example 5 Graph Logarithmic Functions ● |a| = 4: The graph is stretched vertically. ● h = –2: The graph is translated 2 units to the left. ● k = 0: There is no vertical shift.

Example 5 Graph Logarithmic Functions Answer:

Example 5 A. B. C.D.

Example 5 A. B. C.D.