Warmup Alg 2
22 Mar 2012
Agenda
• Don't forget about resources on
mrwaddell.net
• Assignment from last class period
• Sect 7.5: Properties of logarithms
Go over assignment from last
class period
Section 7.5: Properties of
Logarithms
Vocabulary
Exponentials
Any equation of the form
x=(b)y
Logarithm
The opposite of an
exponential equation
y= logb x
log x
No base? It is automatically
base 10!
ln x
“ln” is a shortcut way to write
loge said “log base e”
Property of Logs and Exponents
One-to-One Property of Exponential
Functions and logs
If bx = by, then x = y.
If
logb x = logb y, then
x = y.
Exponents First – Page 330
Exponents First
Product Property
logb (nm) = logbn + logbm
Quotient Property
logb n = logbn – logbm
m
Power Property
p
logbm
== p logbm
THIS IS EASILY THE MOST
IMPORTANT ONE!
Inverse Properties (2 of them)
logb
x
b
=x
b
logb x
x
Practice Problems
Write each expression as a single logarithm.
Then simplify if possible.
log25 + log27
problem
log2 (5∙7)
product property
log2 (35)
finished
Practice Problems
Write each expression as a single logarithm.
Then simplify if possible.
Log536x3
problem
Log536 + Log5x2
product property
Log536 + 2Log5x
Power property
Practice Problems
Write each expression as a single logarithm.
Then simplify if possible.
10𝑥 5
𝑙𝑛 4
𝑦
problem
𝑙𝑛10𝑥 5 − 𝑦 4
quotient property
𝑙𝑛10 + 𝑙𝑛𝑥 5 − 𝑦 4
product property
𝑙𝑛10 + 5𝑙𝑛𝑥 − 𝑦 4
power property
Practice Problems
Write each expression as a single logarithm.
Then simplify if possible.
log48 + log42
problem
log4(16)
product property
log4 (4∙4)
Hmm, what
exponent for 4x =16
2 is the answer!
Practice Problems
Write each expression as a single logarithm.
Then simplify if possible.
log335 - log5125
problem
5log33 – log5(5∙5∙5)
power prop & factoring
5 – log5(5∙5∙5)
Inverse prop
5–3
How many 5’s are
there again?
2 is the answer!
Assignment
Chapter 7.5: 15-30,
33 – 42,
Pick 10 from each section