Worksheets · Precalculus

Precalculus logarithmic equations worksheet

In Precalculus log equations usually have more than one log, so you combine them with the log properties first. Then rewrite in exponential form, solve, and check each answer against the domain of every log.

Also taught in Algebra 2, at its own level and with its own examples.

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Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Logarithmic Equations

Date Period

Solve each equation.

  1. log⁡2(5a−72)=3
  2. log⁡2x+log⁡2(x−2)=3
  3. log⁡10(m+89)=2
  4. log⁡(4x−8)=log⁡(3x−2)
  5. log⁡4(2n+34)=3
  6. log⁡(x+3)−log⁡x=log⁡2
  7. log⁡4(3n−35)=1
  8. log⁡3x+log⁡3(x−6)=3
  9. log⁡2(n−10)=2
  10. log⁡(x+24)−log⁡x=log⁡3
  11. log⁡10(3y+9964)=4
  12. log⁡(x+21)−log⁡x=log⁡4
  13. log⁡2(p−7)=3
  14. log⁡3x+log⁡3(x−24)=4
  15. log⁡4(x+3)=2
  16. log⁡(x+32)−log⁡x=log⁡5
  17. log⁡10(3x+952)=3
  18. log⁡2x+log⁡2(x−16)=9
  19. log⁡2(5y−66)=2
  20. log⁡(x+4)=log⁡(5x−36)

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

Sigma Prep · sigmaprep.io/worksheets

Name

Logarithmic EquationsAnswer keyVersion 1

Date Period

Solve each equation.

  1. log⁡2(5a−72)=3{16}
  2. log⁡2x+log⁡2(x−2)=3{4}
  3. log⁡10(m+89)=2{11}
  4. log⁡(4x−8)=log⁡(3x−2){6}
  5. log⁡4(2n+34)=3{15}
  6. log⁡(x+3)−log⁡x=log⁡2{3}
  7. log⁡4(3n−35)=1{13}
  8. log⁡3x+log⁡3(x−6)=3{9}
  9. log⁡2(n−10)=2{14}
  10. log⁡(x+24)−log⁡x=log⁡3{12}
  11. log⁡10(3y+9964)=4{12}
  12. log⁡(x+21)−log⁡x=log⁡4{7}
  13. log⁡2(p−7)=3{15}
  14. log⁡3x+log⁡3(x−24)=4{27}
  15. log⁡4(x+3)=2{13}
  16. log⁡(x+32)−log⁡x=log⁡5{8}
  17. log⁡10(3x+952)=3{16}
  18. log⁡2x+log⁡2(x−16)=9{32}
  19. log⁡2(5y−66)=2{14}
  20. log⁡(x+4)=log⁡(5x−36){10}

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

How to do these

log⁡2(x)+log⁡2(x−2)=3

  1. Combine with the product rule: log₂(x(x - 2)) = 3.
  2. Exponential form: x² - 2x = 8, so (x - 4)(x + 2) = 0.
  3. x = -2 makes log₂(x) undefined, so it is thrown out.

The answer is x=4.

Where students go wrong

Writing log(x) + log(x - 2) as log(2x - 2). The sum of two logs is the log of the product, x(x - 2), not the log of the sum.

Also called solving log equations, rewriting in exponential form or log equations.

What you can put on this worksheet

A logarithmic equation
log⁡3(v+26)=3 → {1}
Two logs, and extraneous roots
log⁡3x+log⁡3(x−24)=4 → {27}
Isolate first, quadratic inside, ln differences
log⁡12 ⁣(m2+2)=log⁡12(−7m+2) → {−7,0}

Questions about these worksheets

Yes. Every logarithmic equations 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 logarithmic equations 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 three 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.

You pick from 3: a logarithmic equation, two logs, and extraneous roots and isolate first, quadratic inside, ln differences. Tick as many as you want and set how many of each, or let it spread them evenly.

Not checking the answer back in the original. A logarithm cannot take a negative or zero, so a solution that makes the inside of a log negative has to be thrown out even though the algebra produced it.