8.3 Logarithmic Functions What the @#$% does that mean? y=log x b "y equals the logarithm to the base b of x" Properties of Logarithmic Functions The Domain (x) is the set of positive real numbers

The Range (y) is the set of all real numbers

The x-intercept of the graph is 1.

The y-axis is an asymptote of the the graph

The function is a one to one function One to one function? The inverse of the original function is a function as well

This means that the following is true for Logarithmic Functions: y=log x b x=log y b Expressing Numeral Equations in Logarithmic form 7 =49 2 log 49 = 2 7

log 49 = 2 7

base power equals 7 =49 2 base power equals Expressing Logarithmic equations in Exponential/Numeral form So... uh... how do you think logarithmic equations are expressed in Numeral form?

It's just doing the same thing in reverse Evaluating Logarithmic Equations Goals:

To define and graph logarithmic functions

To solve logarithmic equations

y=log x b Quick Review Finding and Graphing Inverses Graph the function Y=X² and find its inverse Y = X²

Set up an "X/Y" chart

Graph the points (0,0) (-1,1) (1,1) (-2,4) (2,4) Exponential/Numeral Form Logarithmic Form Practicing Logarithmic Form ----> Numeral Form Y = logb X X = b Y

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# Logarithmic Functions

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