Review for Math 3 Module 2 Test
Name ________________________
Must show all work.
Date __________ Period ________
Give an example for when log 𝑎 𝑏 = 𝑐
Will equal a negative number
Will equal zero
__________________________
_________________________
Will equal one
Will not exist
__________________________
_________________________
Simplify. Answers must contain only positive exponents.
(6𝑎4 )3
_______________
4 −2
(3) _____________
(3𝑎−2 )−4 _________________
Expand each logarithm. Simplify when possible.
log 2 𝑥𝑦𝑧 _________________________________________________________
𝑥
log 4 𝑧 ___________________________________________________________
log 3 9𝑥 ___________________________________________________________
log 100 3√𝑥 ________________________________________________________
log 2(𝑥 − 6) _______________________________________________________
Evaluate the following logarithms. Justify your answer.
log 2 8
__________
log 5 625 __________
16
log 4 1024 ____________
Solve the following equations.
log 3(𝑥 − 4) − log 3 10 = 0
log2 3𝑥
log2 21
3 log 5 𝑥 = 6 log 5 2
10 𝑥 = 456
=1
Evaluate the following without the use of a calculator. Show all steps.
Given: 𝒍𝒐𝒈𝟐 𝟑 = 𝟏. 𝟓𝟖𝟓
𝒍𝒐𝒈𝟐 𝟓 = 𝟐. 𝟑𝟐𝟐
30
7
𝒍𝒐𝒈𝟐 𝟕 = 𝟐. 𝟖𝟎𝟕
log 2 9 ____________
log 2
log1 12 ____________
log 2 486 _______________
____________
Name 4 points on the graph of 𝑓(𝑥) = log 2 𝑥. Justify your answer.