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Exponents and radicals practice

Change of base formula worksheets

Use a calculator to evaluate natural, common and other logarithms. Choose 12, 14 or 16 questions and round answers to two or three decimal places.

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Evaluate each logarithm with a calculator. Keep full calculator precision until the final answer, then round to the selected number of decimal places.

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Use the same logarithm function twice

Choose 12, 14 or 16 calculator questions and answers rounded to the nearest hundredth or thousandth. The default has 14 questions rounded to hundredths. Questions mix ln, explicit base-ten logarithms and other integer bases.

For a positive argument x and a base b greater than zero and different from one, log base b of x = ln(x) / ln(b). Keep all calculator digits until the final division, then round. An approximation sign distinguishes the rounded decimal from the exact logarithm.

The preview and downloaded PDF use the same resolved questions. Answers follow on separate pages; choose the student-only edition when handing out the exercise.

Learning objective

What this activity builds

Apply the change-of-base formula and round only the final logarithm value to the requested precision.

Worked example

Approximate log base 7 of 25 to the nearest hundredth.

ln(25) / ln(7) is approximately 1.65.

Divide the logarithm of the argument by the logarithm of the base. Use the same logarithm function for both values and round only after dividing.

Teaching notes

Make the practice count

  • Use either ln or common log consistently in the quotient.
  • Keep the argument in the numerator and the base in the denominator.
  • Preserve trailing zeros when the requested precision needs them.
  • Arguments between zero and one give negative answers for these bases.

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Choose your options, update the preview, then download the exact same pages.

Choose the worksheet length and rounding precision. Calculator answers are rounded only at the final step.

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Math SheetNameScore/ 14TeacherDateChange of Base FormulaUse a calculator and the change-of-base formula. Round answers to the nearest hundredth.1.Use a calculator. Round to the nearest hundredth.ln1492.Use a calculator. Round to the nearest hundredth.log1027.43.Use a calculator. Round to the nearest hundredth.log15294.Use a calculator. Round to the nearest hundredth.ln38.95.Use a calculator. Round to the nearest hundredth.log101496.Use a calculator. Round to the nearest hundredth.log541.27.Use a calculator. Round to the nearest hundredth.ln458.Use a calculator. Round to the nearest hundredth.log1025.39.Use a calculator. Round to the nearest hundredth.log139610.Use a calculator. Round to the nearest hundredth.ln49.311.Use a calculator. Round to the nearest hundredth.log102412.Use a calculator. Round to the nearest hundredth.log1524.0math-sheet.comPage 1 / 2
Math SheetNameScore/ 14TeacherDateChange of Base FormulaUse a calculator and the change-of-base formula. Round answers to the nearest hundredth.13.Use a calculator. Round to the nearest hundredth.ln17914.Use a calculator. Round to the nearest hundredth.log1040.5math-sheet.comPage 2 / 2

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