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

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12-Jan-2016Category

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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.