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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, b1) 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 one-to-one 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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