Solving exponential equations with logarithms worksheet

When the two sides cannot be written with the same base, a logarithm is the only way down from the exponent. Answers stay exact rather than rounded.



Sigma Prep · sigmaprep.io/worksheets Name Exponential Equations with Logs Date Period Solve each equation. $5^{x} = 41$ $5^{x} = 90$ $7^{x} = 55$ $5^{x} = 77$ $3^{x} = 90$ $3^{x} = 65$ $2^{x} = 61$ $2^{x} = 48$ $3^{x} = 44$ $3^{x} = 79$ $3^{x} = 50$ $2^{x} = 62$ $5^{x} = 80$ $3^{x} = 51$ $5^{x} = 68$ $7^{x} = 50$ $5^{x} = 63$ $7^{x} = 90$ $2^{x} = 78$ $2^{x} = 57$ 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.

$5^{x} = 41$
$5^{x} = 90$
$7^{x} = 55$
$5^{x} = 77$
$3^{x} = 90$
$3^{x} = 65$
$2^{x} = 61$
$2^{x} = 48$
$3^{x} = 44$
$3^{x} = 79$
$3^{x} = 50$
$2^{x} = 62$
$5^{x} = 80$
$3^{x} = 51$
$5^{x} = 68$
$7^{x} = 50$
$5^{x} = 63$
$7^{x} = 90$
$2^{x} = 78$
$2^{x} = 57$



Sigma Prep · sigmaprep.io/worksheets Name Exponential Equations with LogsAnswer keyVersion 1 Date Period Solve each equation. $5^{x} = 41$ $x = \frac{\log 41}{\log 5}$ $5^{x} = 90$ $x = \frac{\log 90}{\log 5}$ $7^{x} = 55$ $x = \frac{\log 55}{\log 7}$ $5^{x} = 77$ $x = \frac{\log 77}{\log 5}$ $3^{x} = 90$ $x = \frac{\log 90}{\log 3}$ $3^{x} = 65$ $x = \frac{\log 65}{\log 3}$ $2^{x} = 61$ $x = \frac{\log 61}{\log 2}$ $2^{x} = 48$ $x = \frac{\log 48}{\log 2}$ $3^{x} = 44$ $x = \frac{\log 44}{\log 3}$ $3^{x} = 79$ $x = \frac{\log 79}{\log 3}$ $3^{x} = 50$ $x = \frac{\log 50}{\log 3}$ $2^{x} = 62$ $x = \frac{\log 62}{\log 2}$ $5^{x} = 80$ $x = \frac{\log 80}{\log 5}$ $3^{x} = 51$ $x = \frac{\log 51}{\log 3}$ $5^{x} = 68$ $x = \frac{\log 68}{\log 5}$ $7^{x} = 50$ $x = \frac{\log 50}{\log 7}$ $5^{x} = 63$ $x = \frac{\log 63}{\log 5}$ $7^{x} = 90$ $x = \frac{\log 90}{\log 7}$ $2^{x} = 78$ $x = \frac{\log 78}{\log 2}$ $2^{x} = 57$ $x = \frac{\log 57}{\log 2}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Exponential Equations with LogsAnswer keyVersion 1

Date Period

Solve each equation.

$5^{x} = 41$ $x = \frac{\log 41}{\log 5}$
$5^{x} = 90$ $x = \frac{\log 90}{\log 5}$
$7^{x} = 55$ $x = \frac{\log 55}{\log 7}$
$5^{x} = 77$ $x = \frac{\log 77}{\log 5}$
$3^{x} = 90$ $x = \frac{\log 90}{\log 3}$
$3^{x} = 65$ $x = \frac{\log 65}{\log 3}$
$2^{x} = 61$ $x = \frac{\log 61}{\log 2}$
$2^{x} = 48$ $x = \frac{\log 48}{\log 2}$
$3^{x} = 44$ $x = \frac{\log 44}{\log 3}$
$3^{x} = 79$ $x = \frac{\log 79}{\log 3}$
$3^{x} = 50$ $x = \frac{\log 50}{\log 3}$
$2^{x} = 62$ $x = \frac{\log 62}{\log 2}$
$5^{x} = 80$ $x = \frac{\log 80}{\log 5}$
$3^{x} = 51$ $x = \frac{\log 51}{\log 3}$
$5^{x} = 68$ $x = \frac{\log 68}{\log 5}$
$7^{x} = 50$ $x = \frac{\log 50}{\log 7}$
$5^{x} = 63$ $x = \frac{\log 63}{\log 5}$
$7^{x} = 90$ $x = \frac{\log 90}{\log 7}$
$2^{x} = 78$ $x = \frac{\log 78}{\log 2}$
$2^{x} = 57$ $x = \frac{\log 57}{\log 2}$

How to do these

$3^{x} = 20$

20 is not a power of 3, so the bases will not match.
Take the log of both sides.
x log 3 = log 20.

The answer is $x = \frac{\log 20}{\log 3}$ .

Where students go wrong

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.

Also called taking logs of both sides or exponential equations.

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.

Algebra 2 is usually taken around 10th or 11th 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.

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

Exponential Equations with Logs

Exponential Equations with LogsAnswer keyVersion 1

How to do these

Where students go wrong

Questions about these worksheets

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