Warmup Alg 222 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

VocabularyExponentials

Logarithm

log x

ln x

Any equation of the form x=(b)y

The opposite of an exponential equation

y= logb x

No base? It is automatically base 10!“ln” is a shortcut way to writeloge 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 =nm

= logbn – logbm

Power Property

logbmp =THIS IS EASILY THE MOST IMPORTANT ONE!

= p logbm

Inverse Properties (2 of them)

logb bx = x xb xb log

Practice ProblemsWrite each expression as a single logarithm. Then simplify if possible.

log25 + log27

log2 (5∙7)

problem

product property

log2 (35) finished

Practice ProblemsWrite each expression as a single logarithm. Then simplify if possible.

Log536x3

Log536 + Log5x2

problem

product property

Log536 + 2Log5x Power property

Practice ProblemsWrite each expression as a single logarithm. Then simplify if possible.

problem

quotient property

product property

𝑙𝑛 10𝑥5

𝑦 4

𝑙𝑛10 𝑥5− 𝑦4

𝑙𝑛10+ 𝑙𝑛𝑥5−𝑦 4

𝑙𝑛10+5 𝑙𝑛𝑥− 𝑦4 power property

Practice ProblemsWrite each expression as a single logarithm. Then simplify if possible.

log48 + log42

log4(16)

problem

product property

log4 (4∙4) Hmm, what exponent for 4x =16

2 is the answer!

Practice ProblemsWrite each expression as a single logarithm. Then simplify if possible.

log335 - log5125

5log33 – log5(5∙5∙5)

problem

power prop & factoring

Inverse prop

2 is the answer!

5 – log5(5∙5∙5)

5 – 3 How many 5’s are there again?

Assignment

Chapter 7.5: 15-30, 33 – 42,

Pick 10 from each section