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Mathematics LibreTexts

5.3E: 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

This page titled 5.3E: Exercises - Logarithms and Logarithmic Functions is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Rupinder Sekhon and Roberta Bloom via source content that was edited to the style and standards of the LibreTexts platform.

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