3.3 Logarithmic Functions-ANSWER KEY

3.3 Logarithmic Functions-ANSWER KEY -...

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Unformatted text preview: Name___________________________________ 3.3: Logarithmic Functions If x > 0 and b is a positive constant (b 1), then y = logb x if and only if by = x. The exponential form of y = logb x is by = x. The logarithmic form of by = x is y = logb x. 1. Change each equation to its exponential form. a.) 6 = log3 729 b.) -3 = log4 1 64 c.) log10 1,000 = 3 2. Change each equation to its logarithmic form. a.) 7 3 = 343 b.) 8 0 = 1 c.) z = x y Answer the following. 3. State the four basic logarithmic properties given on p. 233 in your text. The function defined by f(x) = log10 x = log x is called the common logarithmic function. The function defined by f(x) = loge x = ln x is called the natural logarithmic function. 4. Use your results from the Section 3.2 handout (problem 2) to graph the following function. f(x) = log4 x y 8 6 4 2 x f(x) -3 -2 -1 0 1 2 -2 -2 -4 -6 -8 2 4 6 8 10 12 14 16 x a.) What is the x-intercept of the graph? b.) Following the graph from left to right, is this function increasing or decreasing? c.) What happens as to f(x) as x approaches 0 from the right? d.) Does the function f have an asymptote? If so, what is it? e.) What is the domain of the function f? 5. Use your results from the Section 3.2 handout (problem 6) to graph the following function. f(x) = ln x y 6 4 x f(x) -3 -2 -1 0 1 2 2 -2 -2 2 4 6 8 x -4 a.) Following the graph from left to right, is this function increasing or decreasing? b.) What happens as to f(x) as x approaches 0 from the right? c.) Does the function f have an asymptote? If so, what is it? d.) What is the domain of the function f? Find the domain of each of the following logarithmic functions, algebraically. Write each domain using interval notation. 6. f(x) = log6(5 - x) 7. J(x) = ln x x - 9 8. R(x) = log x 2 + 8x + 12 Answer Key Testname: 3.3 LOGARITHMIC FUNCTIONS 1. a.) 3 6 = 729 b.) 4 = -3 1 64 c.) 103 = 1,000 2. a.) log7 343 = 3 b.) log8 1 = 0 c.) logx z = y 3. See p. 233 4. 8 6 4 2 -2 -2 -4 -6 -8 2 4 6 8 10 12 14 x y a.) x-intercept: (1, 0) b.) increasing c.) as x approaches 0 from the right, f(x) approaches - d.) the y-axis is a vertical asymptote e.) the domain is the set of all positive real numbers Answer Key Testname: 3.3 LOGARITHMIC FUNCTIONS 5. y 4 2 -2 -2 2 4 6 x -4 a.) increasing b.) as x approaches 0 from the right, f(x) approaches - c.) the y-axis is a vertical asymptote d.) the domain of f is the set of all positive real numbers 6. (-, 5) 7. (-, 0) (9, ) 8. (-, -6) (-2, ) ...
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