Inverses of logarithms worksheet for Algebra 2

A logarithm is an exponential read backwards, which is the whole reason it exists. Swapping one for the other is the entire question.

Also taught in Precalculus, 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.



Sigma Prep · sigmaprep.io/worksheets Name Inverses of Logarithms Date Period Find each inverse, or simplify. Find the inverse of a log or exponential function Find the inverse of $f (x) = 3^{x} - 2$ Find the inverse of $f (x) = 10^{x}$ Find the inverse of $f (x) = \log_{3} (x) + 1$ Find the inverse of $f (x) = 3^{x} + 1$ Find the inverse of $f (x) = \log_{3} (x) - 2$ Find the inverse of $f (x) = \log (x) - 1$ Find the inverse of $f (x) = \log (x)$ Find the inverse of $f (x) = \log_{2} (x)$ Find the inverse of $f (x) = \log_{2} (x) - 2$ Find the inverse of $f (x) = 10^{x} + 2$ Simplify $\log_b b^x$ and $b^{\log_b x}$ $\log 100^{x}$ $3^{\log_{3} 9}$ $e^{\ln 39}$ $10^{\log 47}$ $2^{\log_{2} 41}$ $10^{\log 50}$ $10^{\log 29}$ $7^{\log_{7} 5}$ $3^{\log_{3} 34}$ $10^{\log 25}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Inverses of Logarithms

Date Period

Find each inverse, or simplify.

Find the inverse of a log or exponential function
Find the inverse of $f (x) = 3^{x} - 2$
Find the inverse of $f (x) = 10^{x}$
Find the inverse of $f (x) = \log_{3} (x) + 1$
Find the inverse of $f (x) = 3^{x} + 1$
Find the inverse of $f (x) = \log_{3} (x) - 2$
Find the inverse of $f (x) = \log (x) - 1$
Find the inverse of $f (x) = \log (x)$
Find the inverse of $f (x) = \log_{2} (x)$
Find the inverse of $f (x) = \log_{2} (x) - 2$
Find the inverse of $f (x) = 10^{x} + 2$

Simplify $\log_b b^x$ and $b^{\log_b x}$
$\log 100^{x}$
$3^{\log_{3} 9}$
$e^{\ln 39}$
$10^{\log 47}$
$2^{\log_{2} 41}$
$10^{\log 50}$
$10^{\log 29}$
$7^{\log_{7} 5}$
$3^{\log_{3} 34}$
$10^{\log 25}$



Sigma Prep · sigmaprep.io/worksheets Name Inverses of LogarithmsAnswer keyVersion 1 Date Period Find each inverse, or simplify. Find the inverse of a log or exponential function Find the inverse of $f (x) = 3^{x} - 2$ $f^{- 1} (x) = \log_{3} (x + 2)$ Find the inverse of $f (x) = 10^{x}$ $f^{- 1} (x) = \log (x)$ Find the inverse of $f (x) = \log_{3} (x) + 1$ $f^{- 1} (x) = 3^{x - 1}$ Find the inverse of $f (x) = 3^{x} + 1$ $f^{- 1} (x) = \log_{3} (x - 1)$ Find the inverse of $f (x) = \log_{3} (x) - 2$ $f^{- 1} (x) = 3^{x + 2}$ Find the inverse of $f (x) = \log (x) - 1$ $f^{- 1} (x) = 10^{x + 1}$ Find the inverse of $f (x) = \log (x)$ $f^{- 1} (x) = 10^{x}$ Find the inverse of $f (x) = \log_{2} (x)$ $f^{- 1} (x) = 2^{x}$ Find the inverse of $f (x) = \log_{2} (x) - 2$ $f^{- 1} (x) = 2^{x + 2}$ Find the inverse of $f (x) = 10^{x} + 2$ $f^{- 1} (x) = \log (x - 2)$ Simplify $\log_b b^x$ and $b^{\log_b x}$ $\log 100^{x}$ $2 x$ $3^{\log_{3} 9}$ $9$ $e^{\ln 39}$ $39$ $10^{\log 47}$ $47$ $2^{\log_{2} 41}$ $41$ $10^{\log 50}$ $50$ $10^{\log 29}$ $29$ $7^{\log_{7} 5}$ $5$ $3^{\log_{3} 34}$ $34$ $10^{\log 25}$ $25$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Inverses of LogarithmsAnswer keyVersion 1

Date Period

Find each inverse, or simplify.

Find the inverse of a log or exponential function
Find the inverse of $f (x) = 3^{x} - 2$ $f^{- 1} (x) = \log_{3} (x + 2)$
Find the inverse of $f (x) = 10^{x}$ $f^{- 1} (x) = \log (x)$
Find the inverse of $f (x) = \log_{3} (x) + 1$ $f^{- 1} (x) = 3^{x - 1}$
Find the inverse of $f (x) = 3^{x} + 1$ $f^{- 1} (x) = \log_{3} (x - 1)$
Find the inverse of $f (x) = \log_{3} (x) - 2$ $f^{- 1} (x) = 3^{x + 2}$
Find the inverse of $f (x) = \log (x) - 1$ $f^{- 1} (x) = 10^{x + 1}$
Find the inverse of $f (x) = \log (x)$ $f^{- 1} (x) = 10^{x}$
Find the inverse of $f (x) = \log_{2} (x)$ $f^{- 1} (x) = 2^{x}$
Find the inverse of $f (x) = \log_{2} (x) - 2$ $f^{- 1} (x) = 2^{x + 2}$
Find the inverse of $f (x) = 10^{x} + 2$ $f^{- 1} (x) = \log (x - 2)$

Simplify $\log_b b^x$ and $b^{\log_b x}$
$\log 100^{x}$ $2 x$
$3^{\log_{3} 9}$ $9$
$e^{\ln 39}$ $39$
$10^{\log 47}$ $47$
$2^{\log_{2} 41}$ $41$
$10^{\log 50}$ $50$
$10^{\log 29}$ $29$
$7^{\log_{7} 5}$ $5$
$3^{\log_{3} 34}$ $34$
$10^{\log 25}$ $25$

How to do these

Find the inverse of $f (x) = \log_{3} (x)$

A log undoes an exponential with the same base.
So the inverse raises 3 to the power x.

The answer is $f^{- 1} (x) = 3^{x}$ .

Where students go wrong

Flipping the base and the argument instead of the operation. The inverse of log base 3 of x is 3 to the x, not log base x of 3, which is a different function entirely.

Also called inverse of an exponential function or log and exponential inverses.

What you can put on this worksheet

Logarithms and exponentials undo each other: Find the inverse of $f (x) = 3^{x}$ → $f^{- 1} (x) = \log_{3} (x)$
Simplify an inverse pair: $5^{\log_{5} 29}$ → $29$
Shifts and coefficients inside and in front: Find the inverse:
$y = {(\frac{1}{4})}^{2 x}$ → $y = - \frac{\log_{4} x}{2}$
x as the base, x/n exponents, roots of b^x: Find the inverse: $y = \log_{5} (x - 1) - 4$ → $y = 5^{x + 4} + 1$

Questions about these worksheets

Yes. Every inverses of 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 inverses of 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 two 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: logarithms and exponentials undo each other, simplify an inverse pair, shifts and coefficients inside and in front and x as the base, x/n exponents, roots of b^x. Tick as many as you want and set how many of each, or let it spread them evenly.

Flipping the base and the argument instead of the operation. The inverse of log base 3 of x is 3 to the x, not log base x of 3, which is a different function entirely.

Inverses of logarithms worksheet for Algebra 2

Select your difficulty

Find the inverse of a log or exponential function

Simplify log⁡bbx\log_b b^xlogb​bx and blog⁡bxb^{\log_b x}blogb​x

Find the inverse of a log or exponential function

Simplify log⁡bbx\log_b b^xlogb​bx and blog⁡bxb^{\log_b x}blogb​x

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these inverses of logarithms worksheets free?+

Do the inverses of logarithms worksheets come with an answer key?+

Are these inverses of logarithms worksheets printable?+

What grade are these inverses of logarithms worksheets for?+

Can I get a different version of the same inverses of logarithms worksheet?+

Is this a free alternative to Kuta Software for inverses of logarithms?+

Can I choose how hard the inverses of logarithms questions are?+

What kinds of question are on a inverses of logarithms worksheet?+

What do students get wrong with inverses of logarithms?+

Simplify $\log_b b^x$ and $b^{\log_b x}$

Simplify $\log_b b^x$ and $b^{\log_b x}$