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Mathematics LibreTexts

7.3E: Exercises - Logarithms and Logarithmic Functions

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PROBLEM SET: LOGARITHMS AND LOGARITHMIC FUNCTIONS

Rewrite each of these exponential expressions in logarithmic form:

  1. 34=81
  1. 105=100,000
  1. 52=0.04
  1. 41=0.25
  1. 161/4=2
  1. 91/2=3

Rewrite each of these logarithmic expressions in exponential form:

  1. log5625=4
  1. log2(1/32)=5
  1. log111331=3
  1. log100.0001=4
  1. log644=1/3
  1. lne=12

If the expression is in exponential form, rewrite it in logarithmic form.

If the expression is in logarithmic form, rewrite it in exponential form.

  1. 5x=15625
  1. x=93
  1. log5125=x
  1. log3x=5
  1. log10y=4
  1. ex=10
  1. lnx=1
  1. e5=y

For each equation, rewrite in exponential form and solve for x.

  1. log5(x)=3
  1. log2(x)=2
  1. log10(x)=3
  1. log3(x)=6
  1. log25(x)=1/2
  1. log64(x)=1/3

Evaluate without using your calculator.

  1. ln3e
  1. ln1e2
  1. lne10
  1. log10(10e)

For problems 31 – 38: Evaluate using your calculator. Use the change of base formula if needed

  1. log20
  1. ln42
  1. ln2.9
  1. log0.5
  1. log436
  1. log7100
  1. log1053.5
  1. log1.0672

7.3E: Exercises - Logarithms and Logarithmic Functions is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by LibreTexts.

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