4.2 Logarithmic Functions Graphs of Exponential Functions The graph of f(x) = bx has a characteristic shape. If b > 1, the graph rises quickly. If 0 < b < 1, the graph falls quickly. Unless translated the graph has a y-intercept of 1. Note the domain and range!
Definition of a Logarithm A logarithm, or log, is defined in terms of an exponent: If 52=25 then log525=2 You can say that the log is the exponent we put on 5 to get 25 If bx=a, then logba=x Logarithmic Functions y x = 2 is an exponential equation. equation
Its inverse (solving for y) is called a logarithmic equation. equation Here are the parts of each type of equation: Logarithmic Equation Exponential Equation y y = loga x x=a exponent /logarithm base number Example: Example Solve loga64 = 2 Rewrite in exponential form!
loga64 = 2 base number exponent 2 a = 64 a=+8a=8 Example : Solve log5 x = 3 Rewrite in exponential form: 53 = x x = 125 Graphs of Logarithmic Functions The graph of f(x)=logbx has a characteristic
shape. The domain of the function is {x | x >0} Unless translated, the graph has an x-intercept of 1. Note the domain and range!
How do you graph a logarithmic function? Re-write it as an exponential function and make a T-chart: Example: Graph y = log3 x Rewrite as: x = 3 y = 3x x
y 1/9 1/3 1 3 9 -2 -1 0 1 2
y = log3 x y The logarithm with base 10 is called the common logarithm (this is the one your calculator evaluates with the LOG button) The logarithm with base e is called the natural logarithm (this is the one your calculator evaluates with the LN button)
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