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

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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.