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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

## 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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