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### Transcript of Logarithmic Functions. Objectives To write exponential equations in logarithmic form. To use...

• Logarithmic Functions

• ObjectivesTo write exponential equations in logarithmic form.To use properties of logarithms to expand and condense logarithmic expressions.Dont be afraid of logs!

• Logarithmic FunctionsKey to understanding logarithms:A logarithm is an exponent!ExponentBaseArgument

• Logarithmic Functions

Exponential FormLogarithmic Form

• Logarithmic FunctionsEvaluate:

• Logarithmic FunctionsEvaluate:

• Logarithmic FunctionsEvaluate:

• Logarithmic FunctionsEvaluate:

• Logarithmic FunctionsEvaluate:

• Logarithmic FunctionsEvaluate:

• Logarithmic FunctionsEvaluate:

• Special BasesCommon logNatural log

• Natural LogarithmEvaluate:

• Properties of Logarithms

• Properties of LogarithmsExpand:

• Properties of LogarithmsExpand:ln does not distribute!

• Properties of LogarithmsExpand:

• Properties of LogarithmsExpand:

• Properties of LogarithmsCombine:

• Properties of LogarithmsCombine:

• Properties of LogarithmsCombine:

• Properties of LogarithmsCombine:

• Properties of LogarithmsCombine:

• Solving Equations Using LogsSolve:Solve:

• Solving Equations Using LogsSolve:Solve:

• Solving Equations Using LogsSolve:Solve:

• Solving Equations Using LogsSolve:Solve:

• Using LogarithmsSuppose you deposit money into an account whose annual interest rate is 4% compounded continuously. How long will it take for the money to double?

• Using LogarithmsChris wants to buy a car. It costs \$30,000, and he only has \$27,000. If he invests it in a bank account at 6% interest compounded quarterly, how long will he have to wait before it matures to \$30,000?

• Logarithmic FunctionsConsider:

• Logarithmic Functions

• Logarithmic FunctionsThe inverse of a logarithmic function is an exponential function.

• Logarithmic Functions(red)

• ConclusionA logarithm indicates the exponent to which you raise a certain base in order to produce a given value.

The inverse of logarithmic function is an exponential function.

Logs to the base 10 are written without a base.

Logs to the base e are indicated by the symbol ln.