Pre-Calculus 12 Notes

By: Gen L.

Lesson 1: Graphing Logarithms

Logarithms

Definition of a Logarithm:

Graphing

The logarithm is the inverse of the exponential function.

The Inverse:
New Form:

Characteristics

• Domain & Range:
• x-intercept:
• y-intercept:
• VA:
• HA:

Transformation Form:

• : Horizontal Translation (and VA)
• : Vertical Translation
• : Base
• : Scale Factor

For example:
Try sketching and

Rational Bases

• Bases of logarithms don't have to just be whole numbers.
• Since logarithms are the inverse of exponentiation, the base could (in theory) be any positive value.

Inverse of Exponentiation

• For an exponential function , the inverse function is
• The inverse can be rewritten as a logarithmic function, where
• Like most trancendental functions, logarithms have restrictions.

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