Worksheets · Precalculus

Precalculus inverses of logarithms worksheet

A logarithm is an exponential read backwards, which is the whole reason it exists. Swapping one for the other is the entire question.

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Pick more than one for a sheet that mixes them.

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Name

Inverses of Logarithms

Date Period

Find each inverse.

  1. Find the inverse of f(x)=511x9
  2. Find the inverse of f(x)=412x4
  3. Find the inverse of f(x)=log9(x)+9
  4. Find the inverse of f(x)=log9(x)7
  5. Find the inverse of f(x)=log8(x)7
  6. Find the inverse of f(x)=37x2
  7. Find the inverse of f(x)=log7(x)9
  8. Find the inverse of f(x)=log9(x)+6
  9. Find the inverse of f(x)=58x+3
  10. Find the inverse of f(x)=log7(x)+4
  11. Find the inverse of f(x)=log11(x)+9
  12. Find the inverse of f(x)=log11(x)7
  13. Find the inverse of f(x)=log9(x)5
  14. Find the inverse of f(x)=log11(x)+1
  15. Find the inverse of f(x)=58x9
  16. Find the inverse of f(x)=38x+9
  17. Find the inverse of f(x)=511x+8
  18. Find the inverse of f(x)=37x9
  19. Find the inverse of f(x)=412x
  20. Find the inverse of f(x)=27x+3

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Inverses of LogarithmsAnswer keyVersion 1

Date Period

Find each inverse.

  1. Find the inverse of f(x)=511x9f1(x)=log11(x+95)
  2. Find the inverse of f(x)=412x4f1(x)=log12(x+44)
  3. Find the inverse of f(x)=log9(x)+9f1(x)=9x9
  4. Find the inverse of f(x)=log9(x)7f1(x)=9x+7
  5. Find the inverse of f(x)=log8(x)7f1(x)=8x+7
  6. Find the inverse of f(x)=37x2f1(x)=log7(x+23)
  7. Find the inverse of f(x)=log7(x)9f1(x)=7x+9
  8. Find the inverse of f(x)=log9(x)+6f1(x)=9x6
  9. Find the inverse of f(x)=58x+3f1(x)=log8(x35)
  10. Find the inverse of f(x)=log7(x)+4f1(x)=7x4
  11. Find the inverse of f(x)=log11(x)+9f1(x)=11x9
  12. Find the inverse of f(x)=log11(x)7f1(x)=11x+7
  13. Find the inverse of f(x)=log9(x)5f1(x)=9x+5
  14. Find the inverse of f(x)=log11(x)+1f1(x)=11x1
  15. Find the inverse of f(x)=58x9f1(x)=log8(x+95)
  16. Find the inverse of f(x)=38x+9f1(x)=log8(x93)
  17. Find the inverse of f(x)=511x+8f1(x)=log11(x85)
  18. Find the inverse of f(x)=37x9f1(x)=log7(x+93)
  19. Find the inverse of f(x)=412xf1(x)=log12(x4)
  20. Find the inverse of f(x)=27x+3f1(x)=log7(x32)

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Find the inverse of f(x)=log3(x)

  1. A log undoes an exponential with the same base.
  2. So the inverse raises 3 to the power x.

The answer is f1(x)=3x.

Where students go wrong

Flipping the base and the argument instead of the operation. The inverse of log base 3 of x is 3 to the x, not log base x of 3, which is a different function entirely.

Also called inverse of an exponential function or log and exponential inverses.

Questions about these worksheets

Yes. Every inverses of logarithms sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the inverses of logarithms questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Flipping the base and the argument instead of the operation. The inverse of log base 3 of x is 3 to the x, not log base x of 3, which is a different function entirely.