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Exponents and radicals practice

Meaning of logarithms worksheets

Rewrite exponential and logarithmic equations and evaluate exact logarithms. Choose numeric or symbolic forms, fractional exponents and reciprocal arguments, with separate answers.

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Rewrite each equation in the requested form or evaluate the logarithm exactly. Keep the base, exponent and argument in their corresponding positions.

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Read a logarithm as an exponent

The default sheet has six equations to rewrite in exponential form, six to rewrite in logarithmic form and twelve exact logarithms to evaluate. Choose rewrite-only or evaluation-only practice for a shorter twelve-question sheet.

For b > 0 and b ≠ 1, log base b of a = e means b^e = a. Numeric answers are exact fractions or integers. Symbolic questions include the domain conditions needed to make each logarithm valid.

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Learning objective

What this activity builds

Connect a logarithm with the exponent in the equivalent power equation.

Worked example

Rewrite 8^(1/3) = 2 as a logarithmic equation.

log base 8 of 2 = 1/3.

The logarithm asks which exponent on 8 produces 2. Since the cube root of 8 is 2, that exponent is 1/3.

Teaching notes

Make the practice count

  • Identify the base before moving any symbols.
  • A logarithm returns an exponent, not the powered value.
  • A negative exponent produces a reciprocal of a positive power.
  • Read the printed domain conditions on symbolic equations.

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Math SheetNameScore/ 24TeacherDateThe Meaning of LogarithmsRewrite between logarithmic and exponential form, then evaluate each logarithm exactly.1.Rewrite in exponential form.log1010022.Rewrite in exponential form.log2166133.Rewrite in exponential form.log7116807-54.Rewrite in exponential form.logr811-1·sDomain: real variablesr0r1sRs: real numbers5.Rewrite in exponential form.logqw-4Domain: real variablesq0q1w06.Rewrite in exponential form.log98127.Rewrite in logarithmic form.1021008.Rewrite in logarithmic form.168071579.Rewrite in logarithmic form.8-216410.Rewrite in logarithmic form.pb49Domain: real variablesp0p1bRb: real numbers11.Rewrite in logarithmic form.k4rDomain: real variablesk0k1r012.Rewrite in logarithmic form.1231728math-sheet.comPage 1 / 2
Math SheetNameScore/ 24TeacherDateThe Meaning of LogarithmsRewrite between logarithmic and exponential form, then evaluate each logarithm exactly.13.Evaluate exactly.log101000014.Evaluate exactly.log1024415.Evaluate exactly.log61777616.Evaluate exactly.log3917.Evaluate exactly.log4096818.Evaluate exactly.log5162519.Evaluate exactly.log1522520.Evaluate exactly.log8221.Evaluate exactly.log416422.Evaluate exactly.log122073623.Evaluate exactly.log625524.Evaluate exactly.log131169math-sheet.comPage 2 / 2

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