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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.
x 10 100 1000 10,000 100,000 …
y = log x …
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.
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.
0
10logI
RI
0
70 10logI
I
0
10log70
10 10
I
I
0
7 logI
I
7
0
10I
I
7010 I I
The running vacuum cleaner is about
710 , or 10,000,000
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.