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Worksheets›Algebra 2›Exponential & logarithmic functions›Exponential and logarithmic form

Exponential and Logarithmic Form Worksheets

Free printable worksheets with answer keys. Pick a level, preview the questions, then open the sheet to swap or delete any single question.

Algebra 2CCSS HSF.BF.B.5Answer key includedPDF · Print
Open in generatorStart with an easy sheet

Easy: Exponential to logarithmic

  1. 1.104 = 10000
  2. 2.53 = 125
  3. 3.42 = 16
  4. 4.52 = 25
  5. 5.34 = 81
  6. 6.54 = 625
Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

A logarithm is an exponent: log_b x = y means b^y = x. The base stays the base, the logarithm's value becomes the exponent, and the number inside the log becomes the result of the power. The natural log ln x is the logarithm with base e.

Easy44 = 256Exponential to logarithmicMediumlog5 625 = 4Logarithmic to exponentialHardlog10 1100 = −2Negative exponents and both directions

How to solve it: a worked example

Rewrite each equation in the other form.

  1. Start42 = 16
  2. b^y = x means log_b x = ylog4 16 = 2
  3. Answerlog4 16 = 2

Common mistakes to watch for

  • Swapping the exponent and the result: writing log₂ 3 = 8 for 2³ = 8.
  • Changing the base when rewriting.
  • Losing the negative sign of the exponent.

Tip: tick “Step-by-step answer key” in the generator to print each step for marking.

Related worksheets

Evaluating logarithmsProperties of logarithms (expanding and condensing)Solving exponential equationsSolving logarithmic equationsCompound and continuous interest

FAQ

How do you switch between the two forms?

log_b(x) = y means bʸ = x: the base stays the base and the log's answer is the exponent. log₂ 8 = 3 because 2³ = 8.

What does a negative exponent look like in log form?

5⁻² = 1/25 becomes log₅(1/25) = −2. Logarithms can be negative; the number inside the log can't.

Is every worksheet different?

Yes. Numbers are generated each time, and the answer key is calculated for that sheet. Swap any single question and its answer updates too.

Can I mix exponential and logarithmic form with other skills?

Yes. In the generator, add more skills; each gets its own section on the sheet with its own instructions.

Is it free to print?

Yes. Generating and printing from the browser is free with no sign-up. PDF downloads need a free account.