In Precalculus matching bases is the first thing to try before reaching for logarithms. The bases hide in fractions and roots, so rewrite 1/4 as 2⁻² and √3 as 3^(1/2) before you set the exponents equal.
Also taught in Algebra 2 and Algebra 1, each at its own level and with its own examples.
Select your difficulty
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.
Write both as powers of 2: 2^(3x - 3) = 2^(-2x - 4).
Set the exponents equal: 3x - 3 = -2x - 4.
So 5x = -1.
The answer is x=−51.
Where students go wrong
Multiplying only the first term of the exponent. (2³)^(x - 1) is 2^(3x - 3), not 2^(3x - 1); the power multiplies the whole exponent.
Also called same base, exponential equations not requiring logarithms or equating exponents.
What you can put on this worksheet
An exponential equation, no logarithms needed
3v=243→ {5}
The variable on both sides
9x=3x+5→ {5}
Equal to 1, products of powers, a number in front, fraction answers
5⋅1252m+3=5m+1→ {−59}
Questions about these worksheets
Yes. Every exponential 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 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, the variable on both sides and equal to 1, products of powers, a number in front, fraction answers. Tick as many as you want and set how many of each, or let it spread them evenly.
Reaching for logs before checking the bases. If both sides can be written as powers of the same number there is nothing to take a log of, and doing it anyway turns a one-line question into a mess.