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Logarithm Problem Worksheet - Basic Level

Lesson Plans > Mathematics > Algebra > Functions > Logarithms
 

Logarithm Problem Worksheet - Basic Level

The worksheet below is designed for students who are just learning the fundamental properties of logarithms.

logmab = logma + logmb (logarithm product property)
logm
a
b
= logma - logmb (logarithm quotient property)
logmak = k·logma (logarithm power property)
logab =
logma
logmb
(logarithm change of base property)
logab =
1
logba
(logarithm base switch property)
logm1 = 0 
logmm = 1

Lesson by Mr. Twitchell

Handouts/Worksheets

Logarithm Problems

All problems should be done without the use of the log function on your calculator. You may use the log function to check your answers.

  1. Write ax = m as a log equation.
     
  2. Write log3w = 12 as an exponential equation.
     
  3. Find x such that log2x = 7
     
  4. Find x such that logx729 = 6
     
  5. Find x such that log32710 = x
     
  6. If log13(3x - 2) = 1, find x.
     
  7. If logm(2m - 19) = 0, find logm0.01
     
  8. Give three ordered pairs (a,b) such that logab = 2
     
  9. Find the value of (log225)(log54)
     
  10. Calculate log2
    3
    16

     
  11. If log25 = 2.322, calculate log240
     
  12. Find x if log2x2 + log2x5 = 28
     
  13. If log320 = 2.727 and log37 = 1.771, calculate log3980
     
  14. Find the value of log1007 if log107 = 0.8541 
     
  15. Find x if log5x + log5x2 = 12
     
  16. If logm10 = 0.8977, find m.
     
  17. Find x if log22x - 3log2x = -2
     
  18. Find x if log3x + 10(x2) = 1
     
  19. Find x if log2x = 4logx2 + 3
     
  20. Find x if log2x + log4x  = 9

Logarithm Problems: Answer Key

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