6.3 Logarithms and Logarithmic Functions

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Presentation transcript:

6.3 Logarithms and Logarithmic Functions

Logarithm (Any Base)

Rewriting Logarithmic equations

Rewriting Exponential equations

Evaluating Logarithmic expressions

Common Logarithm (Base 10) Remember? Logarithm (Any Base) Common Logarithm (Base 10) Natural Log (Base e)

Evaluating Common and Natural Logarithms Use calculator:

Inverse Property 1) 2) So, exponential and log functions undo each other

Examples Simplify Simplify = 0 Simplify Simplify = 2

Examples Simplify Simplify = 5 Simplify Simplify = 61

Examples

Finding inverse functions

Parent graphs for log functions y = x 1 y = x

Graph of Natural Log Graph of Common Log y = x y = 10x y = x y = log x y = ex y = ln x y = x y = log x y = 10x y = x 1 Domain: x > 0 Range: All Real Numbers X-intercept: (1, 0) Y-intercept: Does Not Exist Function is Increasing y-axis is vertical asymptote