171S4.3.notebook
April 07, 2010
MAT 171
4.3 Logarithms and Logarithmic Functions
A. Exponential Equations and Logarithmic Form
Logarithmic Functions For positive numbers x and b, with b ≠ 1, y = logb x if and only if x = by
The function is a logarithmic function with base b. The expression y = logb x is simply called a logarithm, and represents the exponent on b that yields x.
B. Finding Common Logarithms and Natural Logarithms
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C. Graphing Logarithmic Functions
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D. Finding the Domain of a Logarithmic Function
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E. Applications of Logarithms
Runway takeoff distance: This relationship can be approximated by the function L(x) = 2085 ln x ­ 14,900, where L( x) represents the required length of a runway in feet, for a plane with x mtw in pounds, where mtw represents maximum allowable takeoff weight.
Memory retention: Under certain conditions, a person’s retention of random facts can be modeled by the equation P(x) = 95 ­ 14 log2 x, where P( x) is the percentage of those facts retained after x number of days.
Altitude & Barometric Pressure: The altitude or height above sea level can be determined by the formula H = (30T + 8000)ln (P0 / P), where H is the altitude in meters for a temperature T in degrees Celsius, P is the barometric pressure at a given altitude in units called centimeters of mercury ( cmHg), and P0 is the barometric pressure at sea level: 76 cmHg.
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Memory retention: Under certain conditions, a person’s retention of random facts can be modeled by the equation P(x) = 95 ­ 14 log2 x, where P( x) is the percentage of those facts retained after x number of days. Find the percentage of facts a person might retain after:
378/100. a. 32 days b. 64 days c. 78 days
Apr 6­7:10 AM
Memory retention: Under certain conditions, a person’s retention of random facts can be modeled by the equation P(x) = 95 ­ 14 log2 x, where P( x) is the percentage of those facts retained after x number of days. Find the percentage of facts a person might retain after:
378/100. a. 32 days b. 64 days c. 78 days
Apr 6­7:10 AM
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