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