6.4 LogFunctions - Sullivan , 8th ed. MAC1140/MAC1147 6-4:...

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Sullivan , 8 th ed. MAC1140/MAC1147 6-4: Logarithmic Functions The inverse function of y = f(x) = a x is x = a y , which is equivalent to the logarithmic function y = log a x . This equivalence is used to convert between logarithmic and exponential functions. If the base is the number e , then x = e y if and only if y = ln x . Write the equation in logarithmic form: Write in exponential form: 1. 16 = 4 2 2. e 2.2 = M 3. log b 4 = 2 4. ln x = 4 Evaluate; if a u = a v , then u = v: 7. Find a so that the graph of f(x) = log a x . 5. log 5 25 3 6. ln e 3 contains the point (32, 8); simplify. y = log a x or x = a y Domain Range x-intercept Vertical asymptote Charac- teristic Passes through a > 1 (0, ) (- , ) (1, 0) y-axis as y - Increasing, one-to-one (1, 0) (a, 1) 0 < a < 1 (0, ) (- , ) (1, 0) y-axis as y →∞ Decreasing one-to-one (1, 0) (a, 1) Graph the given logarithmic function and its inverse; state the domain, range, and any vertical asymptote: 8. f(x) = 3 – ln (x + 2) 9. f(x) = 2 + log 1/2 x x e 3-y - 2 e (3 - x) - 2 = y x = ( 1 / 2 ) y-2 ( 1 / 2 ) x-2 = y 0 -1 1 0 2 1 3 2 4 3
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Sullivan , 8 th ed. MAC1140/MAC1147 6.5: Properties of Logarithms
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This note was uploaded on 01/04/2012 for the course MAC 1147 taught by Professor Staff during the Fall '08 term at Miami Dade College, Miami.

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6.4 LogFunctions - Sullivan , 8th ed. MAC1140/MAC1147 6-4:...

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