6.5 Applications of Common Logarithms

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Presentation transcript:

6.5 Applications of Common Logarithms Objectives: Define and use the common logarithmic function to solve exponential and logarithmic equations. Evaluate logarithmic expressions by using the change-of-base formula. Standard: 2.8.11.N. Solve exponential equations.

Warm Up: 1.51 0.25 -2.30

The base 10 logarithm is called the common logarithm. In general, logarithmic functions are used to assign large values in the domain to small values in the range. x 10 100 1000 10,000 100,000 … y = log x 1 2 3 4 5

Recall from lesson 2.7 that the graph of y = a*f(x) is the graph of y = f(x) stretched by a factor of a. Therefore the graph of y = 10 log x is the graph of y = log x stretched by a factor of 10.

The running vacuum cleaner is about times as loud as the threshold of hearing.

You can use the change-of-base formula to change a logarithmic expression of any base to base 10 so that you can use the LOG key on your calculator.

p. 389 #10-16 even

p. 390: #28-34 Even

Homework: Practice 6.5 Chapter 6 Test FRIDAY!