11.4 Properties of Logarithms. Logarithms A logarithm is an operation, a little like taking the sine of an angle. Raising a constant to a power is called.

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Presentation transcript:

11.4 Properties of Logarithms

Logarithms A logarithm is an operation, a little like taking the sine of an angle. Raising a constant to a power is called exponentiation. There has to be an “undo” button for exponentiation. Logarithms “undo” exponentials, because a logarithm is the inverse operation to exponentiation.

Notation & Forms My notation: The book’s notation:

Properties of Logarithms The set-up: Suppose that m and n are positive numbers and b is a positive number other than 1. Let p be any real number. The following properties hold:

Product Property

Quotient Property

Power Property

Stop Here

Putting it all together Write the following as a sum or difference only:

Change of Base Your calculator is NOT smart! Your calculator only does logs in base 10 or base e. What if you had to compute a log in another base? (happens all the time) Change of base formula:

When Would I Use a Logarithm? We use logarithms to solve for variable exponents. Example: Solve for x.

Example Solve for x.

Classwork Pg. 626 # [2 each section], [3]

Homework Pg. 639 # 17, 19, 21, 23, 25-30