Unit 5: Logarithmic Functions Inverse of exponential functions. “log base 2 of 6” Ex 1: Domain: all real numbers Range: y > 0 “log base b of x” Domain: x > 0 Range: all real numbers “base b to x power” “log base 7 of 12” Ex 2:

Logarithmic and Exponential Conversions Convert each log expression into an exponential expression Convert each exponential expression into a log expression (1) Base is always the base (2) Exponent and Answer switch

Example 1CONVERSION PRACTICE a)__________________ b)__________________ c) ______________ d) ______________ ExponentialLogarithmic f)__________________ f) ______________

Example 1: Continued (Fill In The Blanks) a)__________________ c)__________________ b) ______________ d) ______________ ExponentialLogarithmic e)__________________ f) ______________

Example 2: Find the missing value by conversion a)b) c) d)e) f)

UNIT 5 (10.4): Common Logarithms Common = base 10 logarithms (without subscript 10) “Common Log” is the [log(] button in calculator Example 1: Finding Common Logs & Change of Base A) B)C) “ change of base formula” (for calculator)

Unit 5 (10.5):Base e and Natural Logs, ln(…) Natural Base (e): special irrational number Natural Base Exponential Function: ( inverse of ln ) Natural Logarithm or Natural Log, ln(...) : ( inverse of e ) OR as N approaches infinity of In calculator, e = [2 nd ], [÷]

Example 1Evaluate Natural Bases a) b)c) Example 2Evaluate Natural Logs a) b) c) Example 3Basic Equations a) b)