The percentage of adult height attained by a girl who is x

Fill in each blank so that the resulting statement is true. y logb x is equivalent to the exponential form ______________, x 0, b 0, b 1.

Fill in each blank so that the resulting statement is true. The function f (x) logb x is the ______________ function with base ______________.

Fill in each blank so that the resulting statement is true. logb b ______________

Fill in each blank so that the resulting statement is true. logb 1 ______________

Fill in each blank so that the resulting statement is true. logb bx ______________

Fill in each blank so that the resulting statement is true. blogb x ______________

Fill in each blank so that the resulting statement is true. Using interval notation, the domain of f (x) logb x is ______________ and the range is ______________.

Fill in each blank so that the resulting statement is true. The graph of f (x) logb x approaches, but does not touch, the ______________-axis. This axis, whose equation is ______________, is a/an ______________ asymptote.

Fill in each blank so that the resulting statement is true. The domain of g(x) log2 (5 x) can be found by solving the inequality ______________.

Fill in each blank so that the resulting statement is true. The logarithmic function with base 10 is called the ______________ logarithmic function. The function f (x) log10 x is usually expressed as f (x) ______________.

Fill in each blank so that the resulting statement is true. The logarithmic function with base e is called the ______________ logarithmic function. The function f (x) loge x is usually expressed as f (x) ______________.

In Exercises 18, write each equation in its equivalent exponential form. 4 log2 16

In Exercises 18, write each equation in its equivalent exponential form. 6 log2 64

In Exercises 18, write each equation in its equivalent exponential form. 2 log3 x

In Exercises 18, write each equation in its equivalent exponential form. 2 log9 x

In Exercises 18, write each equation in its equivalent exponential form. 5 logb 32

In Exercises 18, write each equation in its equivalent exponential form. 3 logb 27

In Exercises 18, write each equation in its equivalent exponential form. log6 216 y

In Exercises 18, write each equation in its equivalent exponential form. log5 125 y

In Exercises 920, write each equation in its equivalent logarithmic form. 23 8

In Exercises 920, write each equation in its equivalent logarithmic form. 54 625

In Exercises 920, write each equation in its equivalent logarithmic form. 24 1 16

In Exercises 920, write each equation in its equivalent logarithmic form. 53 1 125

In Exercises 920, write each equation in its equivalent logarithmic form. 3 8 2

In Exercises 920, write each equation in its equivalent logarithmic form. 3 64 4

In Exercises 920, write each equation in its equivalent logarithmic form. 132 x

In Exercises 920, write each equation in its equivalent logarithmic form. 152 x

In Exercises 920, write each equation in its equivalent logarithmic form. b3 1000

In Exercises 920, write each equation in its equivalent logarithmic form. b3 343

In Exercises 920, write each equation in its equivalent logarithmic form. 7y 200

In Exercises 920, write each equation in its equivalent logarithmic form. 8y 300

In Exercises 2142, evaluate each expression without using a calculator. log4 16

In Exercises 2142, evaluate each expression without using a calculator. log7 49

In Exercises 2142, evaluate each expression without using a calculator. log2 64

In Exercises 2142, evaluate each expression without using a calculator. log3 27

In Exercises 2142, evaluate each expression without using a calculator. log5 1 5

In Exercises 2142, evaluate each expression without using a calculator. log6 1 6

In Exercises 2142, evaluate each expression without using a calculator. log2 1 8

In Exercises 2142, evaluate each expression without using a calculator. log3 1 9

In Exercises 2142, evaluate each expression without using a calculator. log77

In Exercises 2142, evaluate each expression without using a calculator. log66

In Exercises 2142, evaluate each expression without using a calculator. log2 1 2

In Exercises 2142, evaluate each expression without using a calculator. log3 1 3

In Exercises 2142, evaluate each expression without using a calculator. log64 8

In Exercises 2142, evaluate each expression without using a calculator. log81 9

In Exercises 2142, evaluate each expression without using a calculator. log5 5

In Exercises 2142, evaluate each expression without using a calculator. log11 11

In Exercises 2142, evaluate each expression without using a calculator. log4 1

In Exercises 2142, evaluate each expression without using a calculator. log6 1

In Exercises 2142, evaluate each expression without using a calculator. log5 57

In Exercises 2142, evaluate each expression without using a calculator. log4 46

In Exercises 2142, evaluate each expression without using a calculator. 8log8 19

In Exercises 2142, evaluate each expression without using a calculator. 7log7 23

Graph f (x) 4x and g(x) log4 x in the same rectangular coordinate system.

Graph f (x) 5x and g(x) log5 x in the same rectangular coordinate system.

Graph f (x) 12 x and g(x) log1 2 x in the same rectangular coordinate system.

Graph f (x) 14 x and g(x) log1 4 x in the same rectangular coordinate system.

In Exercises 4752, find the domain of each logarithmic function. f (x) log5(x 4)

In Exercises 4752, find the domain of each logarithmic function. f (x) log5(x 6)

In Exercises 4752, find the domain of each logarithmic function. f (x) log(2 x)

In Exercises 4752, find the domain of each logarithmic function. f (x) log(7 x)

In Exercises 4752, find the domain of each logarithmic function. f (x) ln(x 2)2

In Exercises 4752, find the domain of each logarithmic function. f (x) ln(x 7)2

In Exercises 5366, evaluate each expression without using a calculator. log 100

In Exercises 5366, evaluate each expression without using a calculator. log 1000

In Exercises 5366, evaluate each expression without using a calculator. log 107

In Exercises 5366, evaluate each expression without using a calculator. log 108

In Exercises 5366, evaluate each expression without using a calculator. 10log 33

In Exercises 5366, evaluate each expression without using a calculator. 10log 53

In Exercises 5366, evaluate each expression without using a calculator. ln 1

In Exercises 5366, evaluate each expression without using a calculator. ln e

In Exercises 5366, evaluate each expression without using a calculator. ln e6

In Exercises 5366, evaluate each expression without using a calculator. ln e7

In Exercises 5366, evaluate each expression without using a calculator. ln 1 e6

In Exercises 5366, evaluate each expression without using a calculator. ln 1 e7

In Exercises 5366, evaluate each expression without using a calculator. eln 125

In Exercises 5366, evaluate each expression without using a calculator. eln 300

In Exercises 6772, simplify each expression. ln e9x

In Exercises 6772, simplify each expression. ln e13x

In Exercises 6772, simplify each expression. eln 5x2

In Exercises 6772, simplify each expression. eln 7x2

In Exercises 6772, simplify each expression. 10log x

In Exercises 6772, simplify each expression. 10log 3 x

In Exercises 7376, write each equation in its equivalent exponential form. Then solve for x. log3(x 1) 2

In Exercises 7376, write each equation in its equivalent exponential form. Then solve for x. log5(x 4) 2

In Exercises 7376, write each equation in its equivalent exponential form. Then solve for x. log4 x 3

In Exercises 7376, write each equation in its equivalent exponential form. Then solve for x. log64 x 2 3

In Exercises 7780, evaluate each expression without using a calculator. log3(log7 7)

In Exercises 7780, evaluate each expression without using a calculator. log5(log2 32)

In Exercises 7780, evaluate each expression without using a calculator. log2(log3 81)

In Exercises 7780, evaluate each expression without using a calculator. log(ln e)

In Exercises 8186, match each function with its graph. The graphs are labeled (a) through (f), and each graph is displayed in a [5, 5, 1] by [5, 5, 1] viewing rectangle. f (x) ln(x 2)

In Exercises 8186, match each function with its graph. The graphs are labeled (a) through (f), and each graph is displayed in a [5, 5, 1] by [5, 5, 1] viewing rectangle. f (x) ln(x 2)

In Exercises 8186, match each function with its graph. The graphs are labeled (a) through (f), and each graph is displayed in a [5, 5, 1] by [5, 5, 1] viewing rectangle. f (x) ln x 2

In Exercises 8186, match each function with its graph. The graphs are labeled (a) through (f), and each graph is displayed in a [5, 5, 1] by [5, 5, 1] viewing rectangle. f (x) ln x 2

In Exercises 8186, match each function with its graph. The graphs are labeled (a) through (f), and each graph is displayed in a [5, 5, 1] by [5, 5, 1] viewing rectangle. f (x) ln(1 x)

In Exercises 8186, match each function with its graph. The graphs are labeled (a) through (f), and each graph is displayed in a [5, 5, 1] by [5, 5, 1] viewing rectangle. f (x) ln(2 x)

The percentage of adult height attained by a girl who is x years old can be modeled by f (x) 62 35 log(x 4), where x represents the girls age (from 5 to 15) and f (x) represents the percentage of her adult height. Use the formula to solve Exercises 8788. Round answers to the nearest tenth of a percent. Approximately what percentage of her adult height has a girl attained at age 13?

The percentage of adult height attained by a girl who is x years old can be modeled by f (x) 62 35 log(x 4), where x represents the girls age (from 5 to 15) and f (x) represents the percentage of her adult height. Use the formula to solve Exercises 8788. Round answers to the nearest tenth of a percent. Approximately what percentage of her adult height has a girl attained at age ten?

The bar graph indicates that the percentage of first-year college students expressing antifeminist views declined after 1970. Use this information to solve Exercises 8990. The function f (x) 7.52 ln x 53 models the percentage of first-year college men, f (x), expressing antifeminist views (by agreeing with the statement) x years after 1969. a. Use the function to find the percentage of first-year college men expressing antifeminist views in 2008. Round to one decimal place. Does this function value overestimate or underestimate the percentage displayed by the graph? By how much? b. Use the function to project the percentage of first-year college men who will express antifeminist views in 2015. Round to one decimal place.

The bar graph indicates that the percentage of first-year college students expressing antifeminist views declined after 1970. Use this information to solve Exercises 8990. The function f (x) 4.82 ln x 32.5 models the percentage of first-year college women, f (x), expressing antifeminist views (by agreeing with the statement) x years after 1969. a. Use the function to find the percentage of first-year college women expressing antifeminist views in 2008. Round to one decimal place. Does this function value overestimate or underestimate the percentage displayed by the graph? By how much? b. Use the function to project the percentage of first-year college women who will express antifeminist views in 2015. Round to one decimal place.

The sound of a blue whale can be heard 500 miles away, reaching an intensity of 6.3 106 watts per meter2. Determine the decibel level of this sound. At close range, can the sound of a blue whale rupture the human eardrum?

What is the decibel level of a normal conversation, 3.2 106 watt per meter2?

Students in a psychology class took a final examination. As part of an experiment to see how much of the course content they remembered over time, they took equivalent forms of the exam in monthly intervals thereafter. The average score for the group, f(t), after t months was modeled by the function f(t) 88 15 ln(t 1), 0 t 12. a. What was the average score on the original exam? b. What was the average score, to the nearest tenth, after 2 months? 4 months? 6 months? 8 months? 10 months? one year? c. Sketch the graph of f (either by hand or with a graphing utility). Describe what the graph indicates in terms of the material retained by the students.

Describe the relationship between an equation in logarithmic form and an equivalent equation in exponential form.

What question can be asked to help evaluate log3 81?

Explain why the logarithm of 1 with base b is 0.

Describe the following property using words: logb bx x.

Explain how to use the graph of f (x) 2x to obtain the graph of g(x) log2 x.

Explain how to find the domain of a logarithmic function.

Logarithmic models are well suited to phenomena in which growth is initially rapid, but then begins to level off. Describe something that is changing over time that can be modeled using a logarithmic function.

Suppose that a girl is 4 feet 6 inches at age 10. Explain how to use the function in Exercises 8788 to determine how tall she can expect to be as an adult.

In Exercises 102105, graph f and g in the same viewing rectangle. Then describe the relationship of the graph of g to the graph of f. f (x) ln x, g(x) ln(x 3)

In Exercises 102105, graph f and g in the same viewing rectangle. Then describe the relationship of the graph of g to the graph of f. f (x) ln x, g(x) ln x 3

In Exercises 102105, graph f and g in the same viewing rectangle. Then describe the relationship of the graph of g to the graph of f. f (x) log x, g(x) log x

In Exercises 102105, graph f and g in the same viewing rectangle. Then describe the relationship of the graph of g to the graph of f. f (x) log x, g(x) log(x 2) 1

Students in a mathematics class took a final examination. They took equivalent forms of the exam in monthly intervals thereafter. The average score, f(t), for the group after t months is modeled by the human memory function f(t) 75 10 log(t 1), where 0 t 12. Use a graphing utility to graph the function. Then determine how many months will elapse before the average score falls below 65.

In parts (a)(c), graph f and g in the same viewing rectangle. a. f (x) ln(3x), g(x) ln 3 ln x b. f (x) log(5x2), g(x) log 5 log x2 c. f (x) ln(2x3), g(x) ln 2 ln x3 d. Describe what you observe in parts (a)(c). Generalize this observation by writing an equivalent expression for logb(MN), where M 0 and N 0. e. Complete this statement: The logarithm of a product is equal to .

Graph each of the following functions in the same viewing rectangle and then place the functions in order from the one that increases most slowly to the one that increases most rapidly. y x, y x, y ex, y ln x, y xx, y x2

In Exercises 109112, determine whether each statement makes sense or does not make sense and explain your reasoning. I estimate that log8 16 lies between 1 and 2 because 81 8 and 82 64.

In Exercises 109112, determine whether each statement makes sense or does not make sense and explain your reasoning. When graphing a logarithmic function, I like to show the graph of its horizontal asymptote.

In Exercises 109112, determine whether each statement makes sense or does not make sense and explain your reasoning. I can evaluate some common logarithms without having to use a calculator.

In Exercises 109112, determine whether each statement makes sense or does not make sense and explain your reasoning. An earthquake of magnitude 8 on the Richter scale is twice as intense as an earthquake of magnitude 4.

In Exercises 113116, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. log2 8 log2 4 8 4

In Exercises 113116, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. log(100) 2

In Exercises 113116, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The domain of f (x) log2 x is ( , ).

In Exercises 113116, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. logb x is the exponent to which b must be raised to obtain x.

Without using a calculator, find the exact value of log3 81 logp 1 log22 8 log 0.001 .

Without using a calculator, find the exact value of log4[log3(log2 8)].

Without using a calculator, determine which is the greater number: log4 60 or log3 40.

Solve the system: 2x 11 5y 3x 2y 12. (Section 4.3, Example 4)

Factor completely: 6x2 8xy 2y2. (Section 6.5, Example 8)

Solve: x 3 4 or 2 7x 16. (Section 9.2, Example 6)

Exercises 123125 will help you prepare for the material covered in the next section. In each exercise, evaluate the indicated logarithmic expressions without using a calculator. a. Evaluate: log2 32. b. Evaluate: log2 8 log2 4. c. What can you conclude about log2 32, or log2(8 4)?

Exercises 123125 will help you prepare for the material covered in the next section. In each exercise, evaluate the indicated logarithmic expressions without using a calculator. a. Evaluate: log2 16. b. Evaluate: log2 32 log2 2. c. What can you conclude about log2 16, or log2 32 2 ?

Exercises 123125 will help you prepare for the material covered in the next section. In each exercise, evaluate the indicated logarithmic expressions without using a calculator. a. Evaluate: log3 81. b. Evaluate: 2 log3 9. c. What can you conclude about log3 81, or log3 92?