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EXPONENTS AND LOGARITHMIC FUNCTIONS Exponents ­ 6 3 6 ­3 = 6 ∙ 6 ∙ 6 = 1/6 3 = 1/(6∙ 6∙ 6) 4 √625 = 4 1/2 8 1/3 x 1/n 125 (36) 5 √16807 = when exponent is fraction = 3 √8 = 2 What number √4 = 2 ∙ What number ∙What number = 8 = n √x 2/3 5/2 = [(125) = [√32] 1/3 2 ] = ( 3 √125) 2 = 5 2 = 25 5 = 6 5 = 7776 1 Exponential Growth and Decay x y = ab a = original amount b = growth or decay rate x = time periods Exponential Growth or Decay? Graph y = 4(2) x x y 2 Logarithmic Functions ­ another way to write exponents Base exponent = Answer 2 Using logs ­ log base log log 5 = 32 answer = exponent 2 32 = 5 3 729 = 6 3 6 = 729 Write in exponential form log 2 16 = 4 log 5 625 = 4 Write in logarithmic form 7 3 4 ­2 8 1/3 10 = 343 = 1/16 3 = 2 = 1000 3 Find the value of n. log 2 n = 4 n = log log 5 125 n 100,000 = 5 log 5 1/5 = n log 6 √6 = n log 81 n = 5/4 log x 8 = 3/4 log 10 1,000,000 = n 4 Common Logarithms are logarithms with base 10 y = log 10 x or y = log x (If there is no base number, use 10) Finding common logs of powers of 10 easy to find without calculator. x log 100 = 10 = 100 x = log 1,000,000 = log .1 = log 1000 = log 10 8 = What if you aren't using powers of 10? CALCULATOR!!!! log 5 = log 12 = log x = 1.5 know this is base 10 10 1.5 = x Writing the problems WILL help!!!! 5 Logarithmic Functions are inverses of exponential functions (exp growth/decay) Graph y = 2 x exponential growth. x y x The inverse of y = 2 is log 2 x = y Don't worry how ­ later mathematics Worry about what a log function will look like!!! 6