Evaluate each expression.
PRACTICE
(1) log 16 _____
(2) log 1 _____
(3) log
(4) log
(5) log 3 _____
(6) log
(8) log
(9) log
_____
(12) log 2
_____
10 _____
(7) log
(10) log
PRACTICE
_____
/
/
(11) log
243 _____
_____
81 _____
_____
/
8 _____
Use the log button on your calculator to evaluate each expression.
(13) log 100 ______
(14) log 10 ______
(15) log 10,000 ______
(16) log 1 ______
(17) log 0.1 ______
(18) log 0.001 ______
(19) Note your answers to
#13—18 What base does the
log button appear to be using?
________
HOW DO YOU KNOW?
PRACTICE
(20) According to the calculator, log 6 ≈ 0.778.
Why is the answer smaller than 1 but greater than zero? ______________________________________
PRACTICE
(21) If log 29 = 𝑥, then x must be between ____ and ____.
WHY?
PRACTICE
(22) If log 625 = 𝑥, then x must be between ____ and ____.
WHY?
PRACTICE
(23) If log
WHY?
PRACTICE
Consider the following information provided. Determine the value of the missing base.
0.5 = 𝑥, then x must be between ____ and ____.
(24) log ____ 16 = 4
log ____ = −3
log ____(2 ∙ 2 ) = 13
BASE:
_______
(25) log ____ 5 = 1/2
log ____
log ____
= −2
BASE:
_______
(26) log ____ 4096 = 4
log ____ 4 = 2/3
log ____ 2
=6
BASE:
_______
=1
PRACTICE
Dr. Tuppersupper has invented his own calculator. It has all of the same digits 0-9, but the
other buttons function differently. For instance, on his calculator, log 10 does not equal 1, as it does
on a normal calculator. Instead, on his calculator, log 10 = 0.926628408. Furthermore, log 100 =
1.853256816 and log 1000 = 2.779885224.
(27) What base is
his calculator using? ______
(28) In the space at right,
prove your answer to #27.
PROOF:
REVIEW
Find the x-intercept(s) of each function.
(30) 5𝑥 − 3𝑦 = −20
(29) 𝑦 = 6𝑥 − 24
x=____
x=____ ____
x=____ ____
(33) 2𝑦 − 4𝑥 = −20
(32) 𝑦 = 5𝑥 + 5𝑥 − 100
(34) 𝑦 = 𝑥 − 2𝑥 − 3
x=____
x=____ ____
REVIEW
(31) 𝑦 = 𝑥 + 2𝑥 − 3
x=____ ____
Write a system of inequalities for each graph below.
(35)
(36)
y
(37)
y
x
x
(38)
y
y
x
x
__________
__________
__________
__________
__________
__________
__________
__________
REVIEW
Factor each expression.
(39) 9𝑥 − 1
(
)(
(40) 3𝑥 + 11𝑥 − 4
)
(42) 9𝑥 − 6𝑥 + 1
(
)(
REVIEW
(
)(
(41) 3𝑥 + 13𝑥 + 4
)
(
(43) 3𝑥 − 13𝑥 + 4
)
(
)(
)(
)
(44) 3𝑥 − 11𝑥 − 4
)
(
)(
)
Let 𝑓(𝑥) = 3𝑥 − 2, 𝑔(𝑥) = 𝑥, ℎ(𝑥) = 4𝑥 − 2𝑥 + 6, 𝑘(𝑥) = 8 − 2𝑥.
(45) 𝑔(𝑓(2))
______
(49) 𝑔(ℎ(𝑥))
_______________
(52) 𝑓(𝑘(𝑥))
_______________
(46) ℎ(𝑔(−4))
______
(47) ℎ(𝑘(2))
______
(50) ℎ(𝑔(𝑥))
_______________
(53) 𝑘(𝑔(𝑥))
_______________
(48) 𝑔(ℎ(−8))
______
(51) 𝑘(𝑓(𝑥))
_______________
(54) 𝑔(𝑘(𝑥))
_______________