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Unformatted text preview: positive numbers m and n: • Log b mn = Log b m + Log b n • Log b m/n = Log b m  Log b n • Log b m n = n Log b m • Log b 1 = 0 • Log b b = 1 Logarithmic Function • The function defined by f(x) = log b x ( b>0, b≠1) is called the logarithmic function with base b. • The domain of f is the set of all positive numbers. Properties of Logarithmic Functions • The function is onetoone • Its range is (infinity, infinity) • Its graph passes through the point (1,0) • It is continuous throughout its domain • It is increasing on (0,infinity) if b>1 and decreasing if b<1. 5. Use the properties of logarithms to expand and simplify the expression log (x(x 2 + 5) 8 ) A property relating e x and ln x: ln e x = x 6. Use logarithms to solve the equation for t: e 0.37t = 11.1 Round your answer to four decimal places 7. If f(x) = log b (x) has the given graph, What is b?...
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 Spring '08
 VAUGHN
 Calculus, Exponential Function, Real Numbers, Derivative, Exponential Functions, Natural logarithm, Logarithm, logb

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