Lecture 4.3 beta bt

Today’s Agenda

Attendance / Announcements

Section 4.3

Quiz on Tuesday

Exam 3 (Chapter 4)

Fri 11/1

The problem…

Solve: x53

What about…

Solve: 53 x

x1412

216 x

We need to apply the same idea to exponential

equations, but what is the inverse?

Logarithms are another way to write exponents

xyby b

x logExponential Form Logarithmic Form

29log3

4log161

2

01log5

38log21

Logarithms are another way to write exponents

xyby b

x logExponential Form Logarithmic Form

2636

21

819

3

81 2

01 e

Evaluating Logarithms

xyby b

x logExponential Form Logarithmic Form

)16(log 2

Evaluating Logarithms

xyby b

x logExponential Form Logarithmic Form

)1(log 5

Evaluating Logarithms

xyby b

x logExponential Form Logarithmic Form

)1000(log10

Evaluating Logarithms

xyby b

x logExponential Form Logarithmic Form

)3(log9

Properties of Logs (pg. 235)

Two Special Logarithms

The Common Logarithm

10loglog"" means

Two Special Logarithms

The Common Logarithm

)100log( )15log(

Two Special Logarithms

The Natural Logarithm

emeans logln""

Two Special Logarithms

The Natural Logarithm

)2ln( )0ln(

Two Special Logarithms

The Natural Logarithm

)2ln( )5.3ln(

Evaluating Logs with Calculator

)8(log3

Evaluating Logs with Calculator

)8(log3

More Properties of Logs (pg. 236)

We use these properties to “expand” and “condense” logarithmic expressions.

More Properties of Logs (pg. 236)

Expand the following logarithmic expressions

)5log( 2 yx

Expand the following logarithmic expressions

z

yx2

ln

Expand the following logarithmic expressions

yz

x5log3

Condense the following logarithmic expressions

yx ln3lnln2

Condense the following logarithmic expressions

zyx log4log2log3

Condense the following logarithmic expressions

2ln4ln2 xx

Classwork / Homework