Properties of Logarithms Today you will use the properties of logarithms to simplify expressions.

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Presentation transcript:

Properties of Logarithms Today you will use the properties of logarithms to simplify expressions.

Like Mr. Carnes, you too may someday enjoy the luxuries that the world of mathematics can bring! Now…for some log fun!

Properties of Logarithms

Product Property

Quotient Property

Powering Property

Use the Properties of Logarithms to expand each expression.

Use the Properties of Logarithms to condense each expression.

Solve each expression.

Solving Equations When solving equations where the variable is in the exponent…...we use logarithms because if we take the log of both sides then we can use the powering property to bring the variable out of the exponent. We use the common and natural logs to solve because those are the values that are programmed into our calculators.

Solve the equation by writing as an exponent then take the log of both sides.

Change of Base Theorem This is just a shortcut, if you take the log of both sides and apply the powering property, you end up with the same result.

Write the expression using only natural logarithms. (same as setting equation = to y and solving using the properties.)

Write the expression using only common logarithms (same as setting equation = to y and solving using the properties).

Assignment A 4.10 Sect III Pgs #3, 7, 9, 14, 16, 22, 29, 30, 33, 34, 43-46, and 54