Exponential and logarithmic equations worksheet for Precalculus

Precalculus equations put the variable in an exponent, often on both sides with different bases, or inside a single log to rewrite in exponential form. Rewriting both sides with a common base is the main move, and log answers should be checked against the domain.

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

Not quite the one you need? Same words, different skill:

Logarithmic Equations (Precalculus). Turning a log equation back into an ordinary one.

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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.



Sigma Prep · sigmaprep.io/worksheets Name Exponential and Logarithmic Equations Date Period Solve each equation. Solve with the variable in one exponent $3^{2 r - 1} = 177147$ $3^{2 v - 6} = \frac{1}{6561}$ $5^{2 v + 1} = 78125$ $3^{2 m + 7} = \frac{1}{19683}$ $6^{2 k - 6} = 1296$ $3^{2 r + 3} = \frac{1}{243}$ $4^{4 y + 3} = 16384$ Solve a logarithmic equation $\log_{5} (2 p + 3085) = 5$ $\log_{4} (8 k - 128) = 3$ $\log_{5} (a + 106) = 3$ $\log_{6} (2 a) = 2$ $\log_{4} (k - 19) = 1$ $\log_{5} (4 p + 37) = 3$ $\log_{4} (5 v - 101) = 1$ Solve with the variable in both exponents $5^{3 x - 1} = 25^{x + 4}$ ${(\frac{1}{5})}^{3 x + 1} = {(\frac{1}{25})}^{2 x + 4}$ $27^{- 2 x - 4} = 9^{x + 2}$ $3^{3 x - 2} = 9^{- x - 1}$ $25^{- x + 3} = 125^{- x - 2}$ ${(\frac{1}{3})}^{- 3 x + 2} = {(\frac{1}{9})}^{- x - 4}$ 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.

Solve with the variable in one exponent
$3^{2 r - 1} = 177147$
$3^{2 v - 6} = \frac{1}{6561}$
$5^{2 v + 1} = 78125$
$3^{2 m + 7} = \frac{1}{19683}$
$6^{2 k - 6} = 1296$
$3^{2 r + 3} = \frac{1}{243}$
$4^{4 y + 3} = 16384$

Solve a logarithmic equation
$\log_{5} (2 p + 3085) = 5$
$\log_{4} (8 k - 128) = 3$
$\log_{5} (a + 106) = 3$
$\log_{6} (2 a) = 2$
$\log_{4} (k - 19) = 1$
$\log_{5} (4 p + 37) = 3$
$\log_{4} (5 v - 101) = 1$

Solve with the variable in both exponents
$5^{3 x - 1} = 25^{x + 4}$
${(\frac{1}{5})}^{3 x + 1} = {(\frac{1}{25})}^{2 x + 4}$
$27^{- 2 x - 4} = 9^{x + 2}$
$3^{3 x - 2} = 9^{- x - 1}$
$25^{- x + 3} = 125^{- x - 2}$
${(\frac{1}{3})}^{- 3 x + 2} = {(\frac{1}{9})}^{- x - 4}$



Sigma Prep · sigmaprep.io/worksheets Name Exponential and Logarithmic EquationsAnswer keyVersion 2 Date Period Solve each equation. Solve with the variable in one exponent $3^{2 r - 1} = 177147$ ${6}$ $3^{2 v - 6} = \frac{1}{6561}$ ${- 1}$ $5^{2 v + 1} = 78125$ ${3}$ $3^{2 m + 7} = \frac{1}{19683}$ ${- 8}$ $6^{2 k - 6} = 1296$ ${5}$ $3^{2 r + 3} = \frac{1}{243}$ ${- 4}$ $4^{4 y + 3} = 16384$ ${1}$ Solve a logarithmic equation $\log_{5} (2 p + 3085) = 5$ ${20}$ $\log_{4} (8 k - 128) = 3$ ${24}$ $\log_{5} (a + 106) = 3$ ${19}$ $\log_{6} (2 a) = 2$ ${18}$ $\log_{4} (k - 19) = 1$ ${23}$ $\log_{5} (4 p + 37) = 3$ ${22}$ $\log_{4} (5 v - 101) = 1$ ${21}$ Solve with the variable in both exponents $5^{3 x - 1} = 25^{x + 4}$ ${9}$ ${(\frac{1}{5})}^{3 x + 1} = {(\frac{1}{25})}^{2 x + 4}$ ${- 7}$ $27^{- 2 x - 4} = 9^{x + 2}$ ${- 2}$ $3^{3 x - 2} = 9^{- x - 1}$ ${0}$ $25^{- x + 3} = 125^{- x - 2}$ ${- 12}$ ${(\frac{1}{3})}^{- 3 x + 2} = {(\frac{1}{9})}^{- x - 4}$ ${10}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Exponential and Logarithmic EquationsAnswer keyVersion 2

Date Period

Solve each equation.

Solve with the variable in one exponent
$3^{2 r - 1} = 177147$ ${6}$
$3^{2 v - 6} = \frac{1}{6561}$ ${- 1}$
$5^{2 v + 1} = 78125$ ${3}$
$3^{2 m + 7} = \frac{1}{19683}$ ${- 8}$
$6^{2 k - 6} = 1296$ ${5}$
$3^{2 r + 3} = \frac{1}{243}$ ${- 4}$
$4^{4 y + 3} = 16384$ ${1}$

Solve a logarithmic equation
$\log_{5} (2 p + 3085) = 5$ ${20}$
$\log_{4} (8 k - 128) = 3$ ${24}$
$\log_{5} (a + 106) = 3$ ${19}$
$\log_{6} (2 a) = 2$ ${18}$
$\log_{4} (k - 19) = 1$ ${23}$
$\log_{5} (4 p + 37) = 3$ ${22}$
$\log_{4} (5 v - 101) = 1$ ${21}$

Solve with the variable in both exponents
$5^{3 x - 1} = 25^{x + 4}$ ${9}$
${(\frac{1}{5})}^{3 x + 1} = {(\frac{1}{25})}^{2 x + 4}$ ${- 7}$
$27^{- 2 x - 4} = 9^{x + 2}$ ${- 2}$
$3^{3 x - 2} = 9^{- x - 1}$ ${0}$
$25^{- x + 3} = 125^{- x - 2}$ ${- 12}$
${(\frac{1}{3})}^{- 3 x + 2} = {(\frac{1}{9})}^{- x - 4}$ ${10}$

How to do these

$4^{x + 1} = 8^{x - 1}$

Write both sides as powers of 2: 2^(2x + 2) = 2^(3x - 3).
Set the exponents equal: 2x + 2 = 3x - 3.
Solve: x = 5.

The answer is ${5}$ .

Where students go wrong

Multiplying the new exponent onto only the first term. (2²)^(x + 1) is 2^(2x + 2), not 2^(2x + 1): the 2 multiplies the whole exponent.

Also called exponential and log equations or log and exponential equations.

What you can put on this worksheet

An exponential equation, no logarithms needed: $3^{v} = 243$ → ${5}$
A logarithmic equation: $\log_{3} (v + 26) = 3$ → ${1}$
Quadratic in b^x: $2^{2 x} - 3 \cdot 2^{x} + 2 = 0$ → ${0, 1}$
The variable on both sides: $9^{x} = 3^{x + 5}$ → ${5}$
Two logs, and extraneous roots: $\log_{3} x + \log_{3} (x - 24) = 4$ → ${27}$
A number log plus a variable log: $\log_{5} 7 + \log_{5} x = \log_{5} 14$ → ${2}$
A quadratic inside, a constant log subtracted: $\log_{5} ⁣ (x^{2} - 30) - \log_{5} 2 = \log_{5} 3$ → ${- 6, 6}$
All ln, the variable subtracted: $\ln 42 - \ln (x + 5) = \ln 6$ → ${2}$

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 8: an exponential equation, no logarithms needed, a logarithmic equation, quadratic in b^x, the variable on both sides, two logs, and extraneous roots, a number log plus a variable log, a quadratic inside, a constant log subtracted and all ln, the variable subtracted. 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.

Exponential and logarithmic equations worksheet for Precalculus

Select your difficulty

Solve with the variable in one exponent

Solve a logarithmic equation

Solve with the variable in both exponents

Solve with the variable in one exponent

Solve a logarithmic equation

Solve with the variable in both exponents

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these exponential and logarithmic equations worksheets free?+

Do the exponential and logarithmic equations worksheets come with an answer key?+

Are these exponential and logarithmic equations worksheets printable?+

What grade are these exponential and logarithmic equations worksheets for?+

Can I get a different version of the same exponential and logarithmic equations worksheet?+

Is this a free alternative to Kuta Software for exponential and logarithmic equations?+

Can I choose how hard the exponential and logarithmic equations questions are?+

What kinds of question are on a exponential and logarithmic equations worksheet?+

What do students get wrong with exponential and logarithmic equations?+