Lesson 3: 6-4 Logarithms and Logarithmic Functions

What is the domain/range/inverse of a logarithmic function?

logarithm
logarithmic function

A.SSE.2 Use the structure of an expression to identify ways to rewrite it.
F.IF.4 For a function that models a relationship between two quantities, interpret dey features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
F.BF.3 Identify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx) and f(x+k) for specific values of k; find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

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The equation y=log(baseb)x is read "y equals the logarithm to the base b of the number x." The base b is always positive and b does not equal 1. Because the equation y=log(base b)x is equivalent to the exponential equation x=b^y, a logarithm is an exponent. It is the exponent that the base b requires in order to equal the number x.

Many scientists believe the extinction of the dinosaurs was caused by an asteroid striking Earth. Astronomers use the Palermo scale to classify objects near Earth based on the likelihood of impact. To make comparing several objects easier, the scale was developed using logarithms. The Palermo scale value of any object can be found using the equations PS=logR, where R is the relative risk posed by the object.

For exercise 62, point out that Betsy is thinking only of logarithmic functions of the form f(x)=alog(base b)x

After discussing the definition of logarithm, write y=2x on the board and ask students to rewrite the equation in with x in terms of y. Repeat for y=x^2. Now write y=2^x on the board and ask students to rewrite this equation with x in terms of y. Students will likely be baffled. Explain that the rewritten equation is x=log(base 2)y. Stress that a logarithm is defined as the invers of an exponential function.

Use McGraw Hill Resources

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