Warmup Alg 216 Feb 2012

Warmup Alg 217 & 21 Feb 2012

Agenda• Don't forget about resources on

mrwaddell.net• Sec 7.4: Intro to logarithms

• Definition of logs• Inverses of logs

Go over assignment from last class period

Section 7.4: Introduction to Logarithms

Vocabulary

Exponentials

Logarithm

Any equation of the form y=(b)x

The opposite of an exponential equation

y=bx if and only if Logby=x

A different look

BASEEXPONENT = POWER (exponential)42 = 16

4 is the base. 2 is the exponent.

16 is the power.

As a logarithm, logBASEPOWER=EXPONENT

log 4 16 = 2

Examples

Write the following in log or exponential form:

27 = 128

log6 1296 = 4

3= log7 343

35 = 243

log2 128 = 7

64 = 129673 = 343log3 243 = 5

Property of Logs and Exponents

One-to-One Property of Exponential Functions

If bx = by, then x = y.

Inverse Properties (2 of them)

logb bx = x xb xb log

log2 28 = 8 5log99 5

Finding Inverses of functions

y=log7x Using the definition of an inverse, becomes:

y=7x

Switch the x and y’s, solve for y

x=log7y

Bcs of the def. of log & exponents

Finding Inverses of functions

y=3x Using the definition of an inverse, becomes:

y=log3x

Switch the x and y’s, solve for y

x=3y

Bcs of the def. of log & exponents

Assignment

Chapter 7.4: pg 503:

8-19,

28-33,

37-41