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Logarithm Problem Worksheet - Basic Level

Lesson Plans > Mathematics > Algebra > Functions > Logarithms

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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_mab = log_ma + log_mb (logarithm product property)
log_m

a

b

= log_ma - log_mb (logarithm quotient property)
log_ma^k = k·log_ma (logarithm power property)
log_ab =

log_ma

log_mb

(logarithm change of base property)
log_ab =

1

log_ba

(logarithm base switch property)
log_m1 = 0
log_mm = 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 log₃w = 12 as an exponential equation.
Find x such that log₂x = 7
Find x such that log_x729 = 6
Find x such that log₃27¹⁰ = x
If log₁₃(3x - 2) = 1, find x.
If log_m(2m - 19) = 0, find log_m0.01
Give three ordered pairs (a,b) such that log_ab = 2
Find the value of (log₂25)(log₅4)
Calculate log₂
3
16
If log₂5 = 2.322, calculate log₂40
Find x if log₂x² + log₂x⁵ = 28
If log₃20 = 2.727 and log₃7 = 1.771, calculate log₃980
Find the value of log₁₀₀7 if log₁₀7 = 0.8541
Find x if log₅x + log₅x² = 12
If log_m10 = 0.8977, find m.
Find x if log²₂x - 3log₂x = -2
Find x if log_{3x + 10}(x²) = 1
Find x if log₂x = 4log_x2 + 3
Find x if log₂x + log₄x = 9

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Logarithm Problems: Answer Key

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