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9.5 – Logarithmic Functions
Key Terms
 Common Logarithm – A logarithm with base 10.
 The common logarithm of x is the power to which 10 must be raised to equal x.
 It is written as , or often simply log x.
 Exponential Equation – An equation that contains an exponential expression.
 Inverse – A function or relation that undoes the work of another function or relation.
 The input of a relation is the same as the output of its inverse.
 Logarithm – The inverse of an exponential expression. is the inverse of , which is the logarithm, base b, of y.
 Logarithmic Equation – An equation that contains a logarithm.
 Logarithmic Function – The inverse of an exponential function.
 In general, the inverse of is , which is the logarithm, base b, of y.
 Natural Logarithm – The logarithm with base e, where .
 The natural logarithm of x is usually written as ln x.
 Vertical Line Test – A method for testing whether a given graph is a function.
 If a vertical line can be drawn that intersects the graph in two or more points, then the graph is not a function.
 If no such line can be drawn, the graph is a function.
Review
Notes
Logarithmic Functions 
 A logarithmic function is the inverse of an exponential function.
 It undoes an exponential function.

 Logarithmic Function Graph

Graphs of Exponential and Logarithmic Functions 
 The graphs of these functions are flipped over the line y = x.
 The x and ycoordinates of each point switches.
 The output of the functions become the input of the inverse functions.



The Relationship Between Logarithms and Exponents 
 Exponential and logarithmic equations are all about multiplication. In both cases:
 b = the number to multiply
 c = the number of times to multiply
 a = the product


Examples
 Ex 1. Which logarithmic equation is equivalent to the exponential equation below?

 Answer:

 Ex 2. Which logarithmic equation is equivalent to the exponential equation below?

 Ex 3. Which exponential equation is equivalent to the logarithmic equation below?
 c = ln 4
 Answer:

 Ex 4. Which logarithmic equation is equivalent to the exponential equation below?

 Ex 5. Which exponential equation is equivalent to the logarithmic equation below?
 log 987 = a
 Answer:

 Ex 6. It is true that the exponential function is the inverse of a logarithmic function.

 Ex 7. Which function is the inverse of ?
 Answer:

Important!
Practice (Apex Study 9.5)
 Try practice problems on Pg 8
 Mandatory: write and answer problems on Pg 9
 1 Quiz
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