Exponential and Logarithmic Functions and Equations

Exponential and Logarithmic Functions and Equations

1. Exponential Functions and Equations

   • General Form
     • rate of change
     • General Characteristics -Doman: {x|x R} -Range: {y|y>0,y R} -y-int: 1 . -H.A: y=0
       • when 0<b<1, decreasing it its domain
       • when b>1, increasing in its doman
     • Inverse
   • Solving Equations
     • changing bases
     • converting to log form
     • exponent laws
   • Applications
     • half life

2. Logarithms

   • General Form
     • General Characteristics -Domain: {x|x>0, x R} -Range: {y|y R} -V.A: x=0 -x-int: 1
       • when 0<b<1, decreasing in its domain
       • when b>1, increasing it its domain
     • Common Log (base 10)
     • y=log x is y equals the log of x to base b
     • y=log x is only valid if x=1
   • Solving Log Equations
     • Extraneous Roots
     • When Quadratics are Obtained Use:
       • quadratic formula
       • factoring
       • pseudo quadtratics
     • Cannot have a negative log
     • Converting To Exponential Form
   • Transformations f(x)=alog[k(x-d)]+c
   • Applications
     • Decibel
     • Richter Scale
     • pH Scale
     • Growth and Decay
     • op Amp
     • Semi-log Plots
     • Compound Interest
   • Laws
     • Law of Roots
     • Quotient Law
     • Product Law
     • Change of Base
     • Power Law
     • if a=b then, loga=logb x =x logx =logx logm