Simplifying Logarithms

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Presentation transcript:

Simplifying Logarithms Honors Precalculus October 27, 2016 Mrs. Agnew

Essential Question Essential Vocabulary What is a logarithm and how do you evaluate logarithms? Essential Vocabulary Exponential Functions Logarithmic Functions Common and Natural Logarithms Change of Base Formula

Definition of Logarithm Inverse of exponential function “Logarithm is an exponent” Definition…

Inverse of Exponentials How do you find the inverse of a function? On the class starter today, we looked at the graphs of inverses of exponential functions. The inverse of exponential functions are logarithmic functions. Graphs Examples…

Simplifying Logarithms To simplify a logarithm, use definition to rewrite as exponential equation. Set logarithm equal to x, convert equation, and find x. Guided Practice Examples

Special Logarithms Common Logarithm Natural Logarithm Logarithm with base of 10 (i.e., log 3) Natural Logarithm Logarithm with base of e (i.e., ln 3) Both can be evaluated on calculator.

Domain of Logarithms The logarithm of a negative number (or 0) does not exist. To find domain, set “big number” greater than zero. Examples…

Change of Base Formula Guided Practice: Page 308 #72 – 78 (Even)

Homework Page 298 Page 309 # 73 – 77 (Odd) #29 – 36, 41, 44, 46, 57, 58, 77, 81, 85, 91, 97, 103, 104 Page 309 # 73 – 77 (Odd)