Logarithmic Functions and Graphs

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Logarithmic Functions.

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Presentation transcript:

Logarithmic Functions and Graphs

Sketch Logarithmic Graphs Use Log Properties Objective Sketch Logarithmic Graphs Use Log Properties

Relevance Log functions are useful for modeling data that represent quantities that increase or decrease slowly. For example, a log function can model the minimum required ventilation rates in public school classrooms.

Warm Up – Make Some Observations

Annually Monthly Quarterly Continuously Warm Up - If $5,000 is invested at an interest rate of 5% per year, find the amount of the investment at the end of 5 years for the following compounding methods: Annually Monthly Quarterly Continuously

Annually: Monthly:

Quarterly: Continuously

Warm Up Solve: Find the Vertex:

Logarithmic Functions

Logarithmic Function It’s the inverse of the exponential function Switch the x’s and the y’s!

Logarithmic Function Used to find unknown exponents in exponential models. Logs define many measurement scales in the sciences: 1) ph 2) decibal 3) Richter scale

For any positive base b, where b≠1: bx = y if and only if x = logby Exponential Form Logarithmic Form

Write in logarithmic form.

Write in logarithmic form.

Write in logarithmic form.

Write in exponential form.

Write in exponential form.

Write in exponential form.

Graphing Log Functions

Graph: Is the inverse of Domain: Range: Domain: Range:

Graph: Up 3 from previous example! Domain: Range:

Left 4 from Original Example! Graph: Left 4 from Original Example! Domain: Range:

Right 2 from Original Example! Graph: Right 2 from Original Example! Domain: Range:

Graph: Reflected over y-axis. Domain: Range:

Graph: Reflected over x-axis. Domain: Range:

Solving Log Functions

Find the value of x.

Find the value of x.

Find the value of x.

Find the value of x.

Find the value of x.

Find the value of x.

Find the value of x.

Find the value of x.

Find the value of x.

Natural Log

Natural log

The Natural Logarithmic Function is the inverse of the natural exponential function Function Inverse

Write in logarithmic form.

Write in exponential form.

Find the value of x.

Using Calculator

Solve

Find to the nearest thousandth – using the calculator.

Find to the nearest thousandth – using the calculator.

Find to the nearest thousandth – using the calculator.