Solving exponential equations with logarithms worksheet for Precalculus

Precalculus equations need algebra before the logarithm: isolating the power when something is added or multiplied, and handling variables in exponents on both sides with different bases. Exact answers are left as a quotient of logs; the rest go to four decimal places.

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

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



Sigma Prep · sigmaprep.io/worksheets Name Exponential Equations with Logs Date Period Solve each equation. Solve exactly with logarithms Find the exact solution, written with $\ln$ : $4 \cdot 3^{x} = 56$ . Solve for $x$ . Give the exact answer in common logs: $2^{x} + 6 = 40$ . Take the common logarithm of both sides and give the exact solution: $2^{x} = 24$ . Solve exactly, using natural logarithms: $3^{x} + 19 = 31$ . Find the exact solution, written with $\log$ : $3^{x} = 5$ . Solve exactly, using natural logarithms: $2 \cdot 2^{x} = 18$ . Solve for $x$ . Give the exact answer in common logs: $2^{x} = 15$ . Isolate the power, then solve Solve to four decimal places: $4 \cdot 3^{x} + 14 = 42$ Solve to four decimal places: $6 \cdot 3^{x} - 3 = 147$ Solve to four decimal places: $2 \cdot 7^{x} + 2 = 32$ Solve to four decimal places: $4 \cdot 2^{x} - 5 = 127$ Solve to four decimal places: $3 \cdot 7^{x} - 2 = 73$ Solve to four decimal places: $4 \cdot 5^{x} + 13 = 117$ Solve to four decimal places: $2 \cdot 5^{x} + 4 = 66$ Solve with different bases Use logarithms to solve, to four decimal places: $2^{x - 2} = 11^{x + 1}$ . Solve for $x$ and round to four decimal places: $5^{x + 3} = 6^{x - 3}$ . Take logs of both sides and solve, to four decimal places: $10^{x - 1} = 3^{x - 4}$ . Find $x$ to four decimal places if $3^{x + 1} = 2^{x + 2}$ . Solve to four decimal places: $5^{x - 4} = 7^{x - 2}$ . Solve for $x$ and round to four decimal places: $3^{x - 4} = 4^{x + 3}$ . Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Exponential Equations with Logs

Date Period

Solve each equation.

Solve exactly with logarithms
Find the exact solution, written with $\ln$ : $4 \cdot 3^{x} = 56$ .
Solve for $x$ . Give the exact answer in common logs: $2^{x} + 6 = 40$ .
Take the common logarithm of both sides and give the exact solution: $2^{x} = 24$ .
Solve exactly, using natural logarithms: $3^{x} + 19 = 31$ .
Find the exact solution, written with $\log$ : $3^{x} = 5$ .
Solve exactly, using natural logarithms: $2 \cdot 2^{x} = 18$ .
Solve for $x$ . Give the exact answer in common logs: $2^{x} = 15$ .

Isolate the power, then solve
Solve to four decimal places: $4 \cdot 3^{x} + 14 = 42$
Solve to four decimal places: $6 \cdot 3^{x} - 3 = 147$
Solve to four decimal places: $2 \cdot 7^{x} + 2 = 32$
Solve to four decimal places: $4 \cdot 2^{x} - 5 = 127$
Solve to four decimal places: $3 \cdot 7^{x} - 2 = 73$
Solve to four decimal places: $4 \cdot 5^{x} + 13 = 117$
Solve to four decimal places: $2 \cdot 5^{x} + 4 = 66$

Solve with different bases
Use logarithms to solve, to four decimal places: $2^{x - 2} = 11^{x + 1}$ .
Solve for $x$ and round to four decimal places: $5^{x + 3} = 6^{x - 3}$ .
Take logs of both sides and solve, to four decimal places: $10^{x - 1} = 3^{x - 4}$ .
Find $x$ to four decimal places if $3^{x + 1} = 2^{x + 2}$ .
Solve to four decimal places: $5^{x - 4} = 7^{x - 2}$ .
Solve for $x$ and round to four decimal places: $3^{x - 4} = 4^{x + 3}$ .



Sigma Prep · sigmaprep.io/worksheets Name Exponential Equations with LogsAnswer keyVersion 2 Date Period Solve each equation. Solve exactly with logarithms Find the exact solution, written with $\ln$ : $4 \cdot 3^{x} = 56$ . $x = \frac{\ln 14}{\ln 3}$ Solve for $x$ . Give the exact answer in common logs: $2^{x} + 6 = 40$ . $x = \frac{\log 34}{\log 2}$ Take the common logarithm of both sides and give the exact solution: $2^{x} = 24$ . $x = \frac{\log 24}{\log 2}$ Solve exactly, using natural logarithms: $3^{x} + 19 = 31$ . $x = \frac{\ln 12}{\ln 3}$ Find the exact solution, written with $\log$ : $3^{x} = 5$ . $x = \frac{\log 5}{\log 3}$ Solve exactly, using natural logarithms: $2 \cdot 2^{x} = 18$ . $x = \frac{\ln 9}{\ln 2}$ Solve for $x$ . Give the exact answer in common logs: $2^{x} = 15$ . $x = \frac{\log 15}{\log 2}$ Isolate the power, then solve Solve to four decimal places: $4 \cdot 3^{x} + 14 = 42$ ${1.7712}$ Solve to four decimal places: $6 \cdot 3^{x} - 3 = 147$ ${2.9299}$ Solve to four decimal places: $2 \cdot 7^{x} + 2 = 32$ ${1.3917}$ Solve to four decimal places: $4 \cdot 2^{x} - 5 = 127$ ${5.0444}$ Solve to four decimal places: $3 \cdot 7^{x} - 2 = 73$ ${1.6542}$ Solve to four decimal places: $4 \cdot 5^{x} + 13 = 117$ ${2.0244}$ Solve to four decimal places: $2 \cdot 5^{x} + 4 = 66$ ${2.1337}$ Solve with different bases Use logarithms to solve, to four decimal places: $2^{x - 2} = 11^{x + 1}$ . $x \approx - 2.2198$ Solve for $x$ and round to four decimal places: $5^{x + 3} = 6^{x - 3}$ . $x \approx 55.9648$ Take logs of both sides and solve, to four decimal places: $10^{x - 1} = 3^{x - 4}$ . $x \approx - 1.7375$ Find $x$ to four decimal places if $3^{x + 1} = 2^{x + 2}$ . $x \approx 0.7095$ Solve to four decimal places: $5^{x - 4} = 7^{x - 2}$ . $x \approx - 7.5665$ Solve for $x$ and round to four decimal places: $3^{x - 4} = 4^{x + 3}$ . $x \approx - 29.7319$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Exponential Equations with LogsAnswer keyVersion 2

Date Period

Solve each equation.

Solve exactly with logarithms
Find the exact solution, written with $\ln$ : $4 \cdot 3^{x} = 56$ . $x = \frac{\ln 14}{\ln 3}$
Solve for $x$ . Give the exact answer in common logs: $2^{x} + 6 = 40$ . $x = \frac{\log 34}{\log 2}$
Take the common logarithm of both sides and give the exact solution: $2^{x} = 24$ . $x = \frac{\log 24}{\log 2}$
Solve exactly, using natural logarithms: $3^{x} + 19 = 31$ . $x = \frac{\ln 12}{\ln 3}$
Find the exact solution, written with $\log$ : $3^{x} = 5$ . $x = \frac{\log 5}{\log 3}$
Solve exactly, using natural logarithms: $2 \cdot 2^{x} = 18$ . $x = \frac{\ln 9}{\ln 2}$
Solve for $x$ . Give the exact answer in common logs: $2^{x} = 15$ . $x = \frac{\log 15}{\log 2}$

Isolate the power, then solve
Solve to four decimal places: $4 \cdot 3^{x} + 14 = 42$ ${1.7712}$
Solve to four decimal places: $6 \cdot 3^{x} - 3 = 147$ ${2.9299}$
Solve to four decimal places: $2 \cdot 7^{x} + 2 = 32$ ${1.3917}$
Solve to four decimal places: $4 \cdot 2^{x} - 5 = 127$ ${5.0444}$
Solve to four decimal places: $3 \cdot 7^{x} - 2 = 73$ ${1.6542}$
Solve to four decimal places: $4 \cdot 5^{x} + 13 = 117$ ${2.0244}$
Solve to four decimal places: $2 \cdot 5^{x} + 4 = 66$ ${2.1337}$

Solve with different bases
Use logarithms to solve, to four decimal places: $2^{x - 2} = 11^{x + 1}$ . $x \approx - 2.2198$
Solve for $x$ and round to four decimal places: $5^{x + 3} = 6^{x - 3}$ . $x \approx 55.9648$
Take logs of both sides and solve, to four decimal places: $10^{x - 1} = 3^{x - 4}$ . $x \approx - 1.7375$
Find $x$ to four decimal places if $3^{x + 1} = 2^{x + 2}$ . $x \approx 0.7095$
Solve to four decimal places: $5^{x - 4} = 7^{x - 2}$ . $x \approx - 7.5665$
Solve for $x$ and round to four decimal places: $3^{x - 4} = 4^{x + 3}$ . $x \approx - 29.7319$

How to do these

Solve to four decimal places: $3 \cdot 2^{x} + 4 = 40$

Subtract 4 and divide by 3: 2^x = 12.
Take the log of both sides: x log 2 = log 12.
x = log 12 ÷ log 2.

The answer is ${3.5850}$ .

Where students go wrong

Taking the log before isolating the power. log(3 · 2^x + 4) cannot be split up, so the 4 and the 3 have to go before the logarithm is applied.

Also called taking logs of both sides.

What you can put on this worksheet

Solve with a logarithm: Solve for $x$ . Give the exact answer in common logs: $3^{x} = 23$ . → $x = \frac{\log 23}{\log 3}$
Isolate the power, then a decimal: Solve to four decimal places: $4 \cdot 5^{x} + 12 = 28$ → ${0.8614}$
Different bases on the two sides: Use logarithms to solve, to four decimal places: $2^{x + 2} = 7^{x}$ . → $x \approx 1.1066$
A constant added, negative exponents, base e: $9^{- 4 m} + 1 = 54$ → ${- 0.4517}$

Questions about these worksheets

Yes. Every solving exponential equations with 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 solving exponential equations with 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 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 4: solve with a logarithm, isolate the power, then a decimal, different bases on the two sides and a constant added, negative exponents, base e. Tick as many as you want and set how many of each, or let it spread them evenly.

Dividing by the base instead of taking a log. From 3 to the x equals 20 you cannot divide by 3: the x is an exponent, not a coefficient, and only a logarithm brings it down.

Solving exponential equations with logarithms worksheet for Precalculus

Solve exactly with logarithms

Isolate the power, then solve

Solve with different bases

Solve exactly with logarithms

Isolate the power, then solve

Solve with different bases

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

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