Worksheets: exponential and logarithmic functionsFunctions · high school

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Answer key · group A · for the teacher · sheet no. 204 517

Exponential and logarithmic functions

1.12.5 mg100% − 50% = 50% ;24 : 8 = 3 ;100 · 0.5 · 0.5 · 0.5 = 12.5

2.(0, +∞)

3.7−(−7) = 7

4.55³ = 125

5.−8646 · 6 · 6 = 216 ;(−4) · 216 = −864

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Answer key

Quiz

Exponential and logarithmic functions

GroupAB

Name Date Score / 15

1.Give the number of days.The half-life of a radioactive isotope is 10 days. After how many days will 160 g of this isotope be reduced to 10 g?(3 pt)

2.For which argument does the function take this value?f(x) = −log₉ x, f(x) = 2(3 pt)

3.Solve the problem using the definition of a logarithm.The pH of a solution is pH = −log[H⁺], where [H⁺] is the concentration of hydrogen ions in mol/dm³. The concentration of hydrogen ions in a solution is 10⁻⁸ mol/dm³. What is the pH of this solution?(3 pt)

4.Give the domain of the function f.The function f is given by the formula f(x) = log₅(x + 4).(2 pt)

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Group B

Quiz

Exponential and logarithmic functions

GroupAB

Name Date Score / 15

1.Give the mass of the drug in milligrams.A patient took 100 mg of a drug. Every 8 hours the body removes 50% of the drug still in it. How many milligrams of the drug will remain in the body after 24 hours?(3 pt)

2.Give the domain of the function:f(x) = 2 · log₈ x(3 pt)

4.Find the base a.The graph of the function f(x) = logₐ x, where a > 0 and a ≠ 1, passes through the point (125, 3).(2 pt)

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Group A

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Quiz6 questions2 groups1 topic

Sheet no.204 517The number is only shown here and on the answer key - never on the student sheet. The same number with the same topics gives the same sheet.

answer key at the endall groups

Quiz

Exponential and logarithmic functions

GroupAB

Name Date Score / 15

2.Give the domain of the function:f(x) = 2 · log₈ x(3 pt)

4.Find the base a.The graph of the function f(x) = logₐ x, where a > 0 and a ≠ 1, passes through the point (125, 3).(2 pt)

5.Compute the value of the function:f(x) = −4 · 6ˣ, f(3) = ?(2 pt)

6.Give the range of the function f.The function f is given by the formula f(x) = (23)ˣ − 3.(2 pt)

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Answer key · group A · for the teacher · sheet no. 204 517

Exponential and logarithmic functions

1.12.5 mg100% − 50% = 50% ;24 : 8 = 3 ;100 · 0.5 · 0.5 · 0.5 = 12.5

2.(0, +∞)

3.7−(−7) = 7

4.55³ = 125

5.−8646 · 6 · 6 = 216 ;(−4) · 216 = −864

6.(−3, +∞)0 − 3 = −3

The method lists the solution steps - handy when going through the sheet with the class.

Maths worksheets · phiboard.comsheet no. 999 999 · answer key, page 10 of 10

Quiz

Exponential and logarithmic functions

GroupAB

Name Date Score / 15

1.Give the number of days.The half-life of a radioactive isotope is 10 days. After how many days will 160 g of this isotope be reduced to 10 g?(3 pt)

2.For which argument does the function take this value?f(x) = −log₉ x, f(x) = 2(3 pt)

4.Give the domain of the function f.The function f is given by the formula f(x) = log₅(x + 4).(2 pt)

5.Compute the value of the function:f(x) = 7 · 4ˣ, f(−2) = ?(2 pt)

6.Give the range of the function f.The function f is given by the formula f(x) = (12)ˣ − 9.(2 pt)

Maths worksheets · phiboard.compage 10 of 10

Answer key · group B · for the teacher · sheet no. 204 517

Exponential and logarithmic functions

1.40160 : 10 = 16 ;2⁴ = 16 ;4 · 10 = 40

2.1812 : (−1) = −2 ;9 · 9 = 81 ;1 : 81 = 181

3.8−(−8) = 8

4.(−4, +∞)x + 4 > 0 ;x > −4

5.7164 · 4 = 16 ;1 : 16 = 116 ;7 · 116 = 716

6.(−9, +∞)0 − 9 = −9

The method lists the solution steps - handy when going through the sheet with the class.

Maths worksheets · phiboard.comsheet no. 999 999 · answer key, page 10 of 10

What goes on the sheet: exponential and logarithmic functions

The generator draws questions from 6 question types in this topic. Every quiz group gets the same types in the same order, only with different numbers, and a practice sheet goes from easier to harder.

Exponential function
Exponential function - base, monotonicity, range
Logarithmic function - base, point of the graph, zero, domain
Logarithmic function
Exponential growth and decay
Logarithmic scales in applications

What the section covers in the curriculum: values and arguments of functions, reading from a graph, properties of functions read from a graph, piecewise functions, linear functions, quadratic functions in general, vertex and factored form, finding the formula of a quadratic, least and greatest values of a quadratic, inverse proportionality, shifting graphs, exponential and logarithmic functions, also in applications

Students can also practise online - the same question types, with step-by-step solutions: Exercises: exponential and logarithmic functions →

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