Top Banner
3.2 and 3.3.notebook 1 October 13, 2015 Feb 141:37 PM • Logarithmic functions are INVERSES of Exponential functions. • They are reflected about the line y=x . X Y X Y inverse of : Dec 1211:08 AM Exponential: Domain: Range: Asymptote: Inverse: Domain: Range: Asymptote:
9
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript

  • 3.2and3.3.notebook

    1

    October13,2015

    Feb141:37PM

    LogarithmicfunctionsareINVERSESofExponentialfunctions.

    Theyarereflectedabouttheliney=x.

    X Y X Y

    inverseof:

    Dec1211:08AM

    Exponential:

    Domain:Range:Asymptote:

    Inverse:

    Domain:Range:Asymptote:

  • 3.2and3.3.notebook

    2

    October13,2015

    Feb141:42PM

    Logarithmic Form Exponential Form

    ifandonlyif

    *** I LOGS***

    3x=27 log4123=x

    Feb141:51PM

    COMMON LOGS have base "10" If no base is listed it means base "10" log 3 means log103 LOG on calc defaults base 10 2nd LOG is 10x is the inverse EXPONENTIAL

    NATURAL LOGS have base "e" If no base is listed it means base "e" "ln" is used for natural logs. ln 4 means loge 4 LN on calc defaults base e 2nd LN is ex inverse EXPONENTIAL

  • 3.2and3.3.notebook

    3

    October13,2015

    Dec1212:16PM

    BasicPropertiesoflogs:

    Dec1212:05PM

    Graph

    Grapheachofthefollowing.Statethedomain,rangeandasymptoteaswellasthetranslationsfromtheparentfunction.

    Examples1:

  • 3.2and3.3.notebook

    4

    October13,2015

    Feb142:05PM

    EXAMPLES2:ChangefromLogarithmicformtoExponentialForm

    EXAMPLES3:ChangefromExponentialtoLogarithmicform

    Feb142:39PM

    EXAMPLES4:Evaluatethefollowing:

  • 3.2and3.3.notebook

    5

    October13,2015

    Feb142:43PM

    EXAMPLES5:Solveforx.

    Feb1410:38AM

    MultiplyingExponentsoftheSameBase

    logbmn=logbm+logbn

    ProductPropertywithlogs

    MoreProperties

    DividingexponentsoftheSameBase Quotient Property with logs

    PowerPropertyofLogarithms

    logbap = p logba

    PowerPropertyofexponents

    (bm)n=bmn

  • 3.2and3.3.notebook

    6

    October13,2015

    Feb1411:21AM

    Expressasasinglelogarithm.Simplifyifpossible.

    1.lnx+ln4 2.log10 250+log10 40

    EXAMPLES6:

    3.log4128log48 4.lnzlnx

    Feb1412:37PM

    Example7Expressasaproduct.Simplifyifpossible.

    1.log104 2.log5252

  • 3.2and3.3.notebook

    7

    October13,2015

    Dec1610:41AM

    EXAMPLES8:

    Expressasasinglelog

    Expand

    Oct138:58AM

    Homework:

    P.2005559oddalsostateasymptoteandEBofg(x)

    P.207209

    13,15,59,61,63,81,83

    93105odd,111118all,121

  • 3.2and3.3.notebook

    8

    October13,2015

    Oct1310:12AM

  • Attachments

    Day2Worksheetanswers.pdf

  • SMART Notebook

    Page 1Page 2Page 3Page 4Page 5Page 6Page 7Page 8Attachments Page 1