# Logarithm Problem Worksheet - Basic Level

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## Logarithm Problem Worksheet - Basic Level

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

log_{m}ab = log

_{m}a + log

_{m}b (logarithm product property)

log

_{m}

a

b

_{m}a - log

_{m}b (logarithm quotient property)

log

_{m}a

^{k}= k·log

_{m}a (logarithm power property)

log

_{a}b =

log

_{m}alog

_{m}blog

_{a}b =

1

log

_{b}alog

_{m}1 = 0

log

_{m}m = 1

Lesson by Mr. Twitchell

## Handouts/Worksheets

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## 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.*

- Write a
^{x}= m as a log equation.

- Write log
_{3}w = 12 as an exponential equation.

- Find x such that log
_{2}x = 7

- Find x such that log
_{x}729 = 6

- Find x such that log
_{3}27^{10}= x

- If log
_{13}(3x - 2) = 1, find x.

- If log
_{m}(2m - 19) = 0, find log_{m}0.01

- Give three ordered pairs (a,b) such that log
_{a}b = 2

- Find the value of (log
_{2}25)(log_{5}4)

- Calculate log
_{2}316

- If log
_{2}5 = 2.322, calculate log_{2}40

- Find x if log
_{2}x^{2}+ log_{2}x^{5}= 28

- If log
_{3}20 = 2.727 and log_{3}7 = 1.771, calculate log_{3}980

- Find the value of log
_{100}7 if log_{10}7 = 0.8541

- Find x if log
_{5}x + log_{5}x^{2}= 12

- If log
_{m}10 = 0.8977, find m.

- Find x if log
^{2}_{2}x - 3log_{2}x = -2

- Find x if log
_{3x + 10}(x^{2}) = 1

- Find x if log
_{2}x = 4log_{x}2 + 3

- Find x if log
_{2}x + log_{4}x = 9

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## Logarithm Problems: Answer Key

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