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Unformatted text preview: Skills Refresher Ch. 5 pg. 219 Logarithms Chapter 5 Logarithmic Functions 5.1 LOGARITHMS AND THEIR PROPERTIES Key Points Using logarithms to solve exponential equations The definition of the logarithm function The equivalence of exponential and logarithmic expressions The inverse relationship between the y = log(x) and y = 10x What is a Logarithm? If x is a positive number, log x is the exponent of 10 that gives x . In other words, if y = log x then 10 y = x . If x is a positive number, log x is the exponent of 10 that gives x . In other words, if y = log x then 10 y = x . Functions Modeling Change: A Preparation for Calculus, 4th Evaluate each of the following. Evaluate each of the following. log10 log10 log 100 log 100 log 1000 log 1000 log 10000 log 10000 log (1/10) log (1/10) log (1/100) log (1/100) log (1/1000) log (1/1000) log 1 log 1 1 1 because 10 because 10 1 = 10 = 10 2 2 because 10 because 10 2 = 100 = 100 3 3 because 10 because 10 3 = 1000 = 1000 4 4 because 10 because 10 4 = 10000 = 10000 1 1 because 10 because 1011 = 1/10 = 1/10 2 2 because 10 because 1022 = 1/100 = 1/100 3 3 because 10 because 1033 = 1/1000 = 1/1000 because 10 because 10 = 1 = 1 Graph of Graph of f f ( ( x x ) = log ) = log x x x f ( x ) .012 .11 1 10 1 100 2 Note that the graph of Note that the graph of y y = log = log x x is the is the graph of y = 10 graph of y = 10 x x reflected through the reflected through the line line y y = = x x . This suggests that these are . This suggests that these are inverse functions. inverse functions. Solving Exponential Equations Solving Exponential Equations Using The Inverse Property Using The Inverse Property log( log(10 x ) = x Solve Solve the equation 10 the equation 10 x = 35 = 35 Take the common log of both sides Take the common log of both sides log log 10 10 x = log 35 = log 35 Using the inverse property log( Using the inverse property log(10 x ) = x this simplifies to x = log 35 Using the calculator to estimate log 35 we have x 1.54 Solving Logarithmic Equations Solving Logarithmic Equations Using The Inverse Property Using The Inverse Property 10 10 log log x x = = x x Solve Solve...
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This note was uploaded on 04/04/2012 for the course MATH 2412 taught by Professor Staff during the Spring '08 term at Austin CC.
 Spring '08
 Staff
 Equations, Logarithmic Functions

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