7.3 Logarithmic Functions as Inverses Objective(s): To write and evaluate logarithmic expressions To graph logarithmic functions.

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Presentation transcript:

7.3 Logarithmic Functions as Inverses Objective(s): To write and evaluate logarithmic expressions To graph logarithmic functions

What are logarithms? ›Logarithms provides a way to work with the inverse of exponential functions. That is, the inverse of the exponential function is the logarithmic function. By definition y = b x is equivalent to log b y = x. ›Exponential function model what some might call “explosive” growth, but logarithmic values grow very slowly. ›Decibels are logarithms that measure sound and when sound energy increase dramatically, the decibel values creep upward. A few extra decibels can bust your eardrums! ›As inverse functions, the domain of y = log b x is the range of y = b x, and the range of y = log b x is the domain of y = b x. ›Logarithms exist only for positive real numbers, which makes sense when you consider that the range of exponential functions is always positive.

Writing Exponential Equations in Logarithmic Form What is the logarithmic form of each equation? ›100 = 10 2 ›81 = 3 4

Writing Exponential Equations in Logarithmic Form What is the logarithmic form of each equation? A 36 = 6 2 BC 1 = 3 0

Evaluating a Logarithm What is the value of log 8 32?

Evaluating a Logarithm What is the value of each logarithm? A log5125 B log432 C

Using a Logarithmic Scale

In 1995, an earthquake in Mexico registered 8.0 on the Richter scale. In 2015 an earthquake of magnitude 4.1 shook Arizona. How many times more intense was the 1995 earthquake than the 2015 earthquake?

Graphing a Logarithmic Function What is the graph of y = log 3 x? Describe the domain and range and identify the y-intercept and the asymptote.

Graphing a Logarithmic Function What is the graph of y = log 4 x? Describe the domain and range and identify the y-intercept and the asymptote.

Translating y = log b x How does the graph of y = log 4 (x-3) + 4 compare to the graph of the parent function.

Translating y = log b x How does the graph of each function compare to the graph of the parent function? ›y = log 2 (x-3) + 4 ›y = 5log 2 x