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Writing logs in terms of others worksheets

Use three given logarithms to find another value without a calculator. Select nine forms and practice with numbers, letters or a mix of both.

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Use the three given logarithms to find each value without a calculator. For numeric questions, combine the supplied rounded values; for letter questions, give an exact expression.

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Build a new logarithm from known values

Each question supplies three logarithms. Factor the target argument and use product, quotient and power laws to combine the known values. Some forms also use the fact that log base b of b equals one.

Choose any of nine forms and numeric, letter or mixed practice. Every sheet has 24 questions; mixed practice gives twelve numeric estimates followed by twelve exact letter expressions. Numeric answers use the provided rounded values, so a fresh calculator evaluation may differ.

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

Recognize products, quotients and powers in a logarithm argument, then express its value using the supplied logarithms.

Worked example

Given log base 10 of 5 is approximately 0.7 and log base 10 of 7 is approximately 0.8, estimate log base 10 of 7/125.

0.8 - 3(0.7) = -1.3, so the requested logarithm is approximately -1.3.

Recognize 125 as 5 cubed. The quotient rule gives log(7) - log(125), then the power rule gives log(7) - 3 log(5). Use the supplied rounded values.

Teaching notes

Make the practice count

  • Factor the target argument before using a logarithm law.
  • All given logarithms in a question share the same base.
  • Remember that the logarithm of its own base is one.
  • Numeric answers are estimates from the provided values, which can differ from a fresh calculator result.

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

Choose forms and numeric or letter givens. Use the supplied values without a calculator; mixed practice has twelve of each.

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Configured PDF · Writing Logs in Terms of Others · US Letter

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Math SheetNameScore/ 24TeacherDateWriting Logs in Terms of OthersUse logarithm properties and the three supplied values. Numeric answers are estimates from the displayed tenths; no calculator is required.1.Use the supplied rounded values. No calculator is required.log870.9log840.7log8101.1log8742.Use the supplied rounded values. No calculator is required.log242.0log293.2log231.6log21693.Use the supplied rounded values. No calculator is required.log481.5log471.4log491.6log42244.Use the supplied rounded values. No calculator is required.log1080.9log1060.8log1030.5log10532math-sheet.comPage 1 / 6
Math SheetNameScore/ 24TeacherDateWriting Logs in Terms of OthersUse logarithm properties and the three supplied values. Numeric answers are estimates from the displayed tenths; no calculator is required.5.Use the supplied rounded values. No calculator is required.log791.1log740.7log7101.2log717296.Use the supplied rounded values. No calculator is required.log740.7log750.8log720.4log7407.Use the supplied rounded values. No calculator is required.log520.4log581.3log571.2log548.Use the supplied rounded values. No calculator is required.log7101.2log791.1log740.7log790math-sheet.comPage 2 / 6
Math SheetNameScore/ 24TeacherDateWriting Logs in Terms of OthersUse logarithm properties and the three supplied values. Numeric answers are estimates from the displayed tenths; no calculator is required.9.Use the supplied rounded values. No calculator is required.log730.6log791.1log750.8log7124310.Use the supplied rounded values. No calculator is required.log870.9log820.3log840.7log85611.Use the supplied rounded values. No calculator is required.log320.6log381.9log392.0log31212.Use the supplied rounded values. No calculator is required.log591.4log530.7log561.1log51math-sheet.comPage 3 / 6
Math SheetNameScore/ 24TeacherDateWriting Logs in Terms of OthersUse logarithm properties and the three supplied values. Numeric answers are estimates from the displayed tenths; no calculator is required.13.Write the logarithm in terms of A, B, and C.log53Alog54Blog59Clog531614.Write the logarithm in terms of A, B, and C.log65Alog64Blog69Clog6112515.Write the logarithm in terms of A, B, and C.log54Alog510Blog59Clog520016.Write the logarithm in terms of A, B, and C.log92Alog97Blog96Clog98417.Write the logarithm in terms of A, B, and C.log68Alog610Blog67Clog680math-sheet.comPage 4 / 6
Math SheetNameScore/ 24TeacherDateWriting Logs in Terms of OthersUse logarithm properties and the three supplied values. Numeric answers are estimates from the displayed tenths; no calculator is required.18.Write the logarithm in terms of A, B, and C.log104Alog109Blog102Clog106419.Write the logarithm in terms of A, B, and C.log910Alog98Blog95Clog925220.Write the logarithm in terms of A, B, and C.log89Alog810Blog83Clog8872921.Write the logarithm in terms of A, B, and C.log76Alog79Blog78Clog72322.Write the logarithm in terms of A, B, and C.log105Alog109Blog107Clog1059math-sheet.comPage 5 / 6
Math SheetNameScore/ 24TeacherDateWriting Logs in Terms of OthersUse logarithm properties and the three supplied values. Numeric answers are estimates from the displayed tenths; no calculator is required.23.Write the logarithm in terms of A, B, and C.log47Alog43Blog42Clog434324.Write the logarithm in terms of A, B, and C.log95Alog910Blog92Clog9100math-sheet.comPage 6 / 6

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