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LEQ: HOW DO YOU EVALUATE COMMON LOGARITHMS? Common Logarithms Sec. 9-5
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The inverse of y = 10 x Switch x and y x = 10 y To solve for y, we define a new function Definition: y is the logarithm of x to the base of 10, or log of x to the base 10 written if and only if 10 y = x. Therefore, the inverse of f(x) = 10 x can be written x = 10 y y = log 10 x f -1 (x) = log 10 x
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Common Logarithms Logarithms with base 10 Often write common logs without indicating the base log 10 x = log x A common logarithm is the exponent to which 10 is raised to get the desired value Can evaluate common logs for any positive real number To evaluate a common log, write the number with base 10 The exponent on 10 is the common log
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Evaluating Common Logarithms Without a calculator: 1.) log 100 = log 10 2 = 2 2.) log.1 = log (1/10) = log 10 -1 = -1 3.)
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Common Logarithm Function Is the inverse of the exponential function Reflections of each other over the line y = x. Domain: the set of positive real numbers Range: the set of all real numbers Never touches the y-axis The y-axis is an asymptote of the graph The x-intercept is 1
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Solving Logarithmic Equations Use the definition of common logarithms Solve log x = 1.5 By definition, x = 10 1.5 Therefore, x ≈ 31.62
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Your Turn Lesson Master 9-5A #1-6, 8, 10, 13-15
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Homework Pgs. 561-562 #2-4, 6-25, 28, 29
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