Logarithmic Functions PRE-CALCULUS UNIT 3: EXPONENTIAL AND LOGARITHMIC FUNCTIONS

Overview of Logarithmic Functions

What is a logarithmic function?

Where do you see logarithmic functions?  Intensity of sound  Intensity of light  Richter Scale  Growth functions  pH levels  Radioactive Decay  Carbon Dating

Relating Logarithmic and Exponential Forms

 Evaluate:  Log 3 81  Log 5 √5

Basic Properties of Logarithms

Apply Properties of Logarithms

Common Logarithm

Graphs of Logarithms

Graphs of Logarithmic Functions  Given the parent logarithmic function y = log x, find:  Domain and Range  X and Y intercepts  Asymptotes  End Behavior  Increasing and Decreasing  Maximums and Minimums

Logarithmic Growth Graph  Where y = log b x and b > 1  Domain and Range  X and Y intercepts  Asymptotes  End Behavior  Increasing and Decreasing  Maximums and Minimums

Logarithmic Decay Graph  Where y = log b x and 0 < b < 1  Domain and Range  X and Y intercepts  Asymptotes  End Behavior  Increasing and Decreasing  Maximums and Minimums

Using Logarithmic Functions

Solve

 The amount of light A absorbed by a sample solution is given by A = 2 – log 100T, where T is the fraction of the light transmitted through the solution.  If the percent of light transmitted through the first sample is 72%, how much light does the sample solution absorb to the nearest hundredth?  If the absorption of the second sample solution is.174, what percent of the light entering the solution is transmitted?