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 Depdendent Variable

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 Dependent Variable

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Properties of Common Logs

 Name Property Example Log of a Product log uv = log u + log v log 5x = log 5 + log x Log of a Quotient Log of a Power log un = n Â· log u log 42 = 2 Â· log 4 10 log u = u 10 log 7 = 7

Here are three special cases involving common logs:

â€¢ log1 = log10 1 = 0 because 100 = 1.

â€¢ log10 = log10 10 = 1 because 101 = 10.

â€¢ log10n = log10 10n = n because log10n = n Â· log 10 = n Â· 1 = n.

Example 1

Write as an equation containing two logs.

Solution

 The right side contains the log of quotient. Use the Log of Quotient Property. L = 10 Â· (log I - log I0)

So can be written as L = 10 Â· (log I - log I0).

Note:

Notice that logI - logI0 must be in parentheses since was multiplied by 10.