Worksheets · Precalculus

Precalculus exponential and logarithmic equations worksheet

Both sheets come down to one idea: a logarithm and an exponential undo each other. The exponential questions all work by writing both sides with the same base, so no calculator is needed anywhere.

Select your difficulty

Pick more than one for a sheet that mixes them.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Exponential and Logarithmic Equations

Date Period

Solve each equation.

  1. 24a+7=1512
  2. log⁡6(8a+56)=3
  3. 22p−6=1256
  4. log⁡2(5n−107)=3
  5. 32b+2=181
  6. log⁡3(6p−123)=1
  7. 32n+7=12187
  8. log⁡6(3y+150)=3
  9. 62y−7=1216
  10. log⁡5(6k+3017)=5
  11. 62a+2=136
  12. log⁡4(6n−110)=2
  13. 25v+2=18192
  14. log⁡10(2m+56)=2
  15. 32v−1=1243
  16. log⁡5(5a−100)=1
  17. 52b−2=125
  18. log⁡3(3v+171)=5
  19. 54k−3=1125
  20. log⁡3(8b+99)=5

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

Sigma Prep · sigmaprep.io/worksheets

Name

Exponential and Logarithmic EquationsAnswer keyVersion 1

Date Period

Solve each equation.

  1. 24a+7=1512{−4}
  2. log⁡6(8a+56)=3{20}
  3. 22p−6=1256{−1}
  4. log⁡2(5n−107)=3{23}
  5. 32b+2=181{−3}
  6. log⁡3(6p−123)=1{21}
  7. 32n+7=12187{−7}
  8. log⁡6(3y+150)=3{22}
  9. 62y−7=1216{2}
  10. log⁡5(6k+3017)=5{18}
  11. 62a+2=136{−2}
  12. log⁡4(6n−110)=2{21}
  13. 25v+2=18192{−3}
  14. log⁡10(2m+56)=2{22}
  15. 32v−1=1243{−2}
  16. log⁡5(5a−100)=1{21}
  17. 52b−2=125{0}
  18. log⁡3(3v+171)=5{24}
  19. 54k−3=1125{0}
  20. log⁡3(8b+99)=5{18}

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

How to do these

2x+1=32

  1. Write 32 as a power of 2: it is 2⁵.
  2. Same base, so the exponents match.
  3. x + 1 = 5.

The answer is x=4.

Where students go wrong

Taking the log of one side only, or forgetting what the answer means. In log₂(x + 3) = 4 the 4 is the exponent, so x + 3 = 2⁴ = 16. Students who write x + 3 = 4 have undone nothing.

Also called solving exponential equations or solving log equations.

What you can put on this worksheet

An exponential equation, no logarithms needed
3v=243 → {5}
A logarithmic equation
log⁡3(v+26)=3 → {1}
Quadratic in b^x
22x−3⋅2x+2=0 → {0,1}

Questions about these worksheets

Yes. Every exponential and 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 exponential and 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: an exponential equation, no logarithms needed, a logarithmic equation and quadratic in b^x. Tick as many as you want and set how many of each, or let it spread them evenly.

Taking the log of one side only, or forgetting what the answer means. In log₂(x + 3) = 4 the 4 is the exponent, so x + 3 = 2⁴ = 16. Students who write x + 3 = 4 have undone nothing.