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5.1_and__5.2_with_space - positive numbers m and n • Log...

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5.1, Exponential Functions Exponential Functions The domain of f is the set of all real numbers. The function defined by f(x) = b x (b>0,but b≠1) is called an exponential function with base b and exponent x. Properties of the Exponential Function The function is one-to-one. The range is (0, infinity). Its graph passes through the point (0,1). It is continuous throughout its domain. It is increasing throughout its domain if b>1 and decreasing throughout its domain if b<1. The function f(x) = e x is called the Natural Exponential Function. Its graph lies between the graphs of y = 2 x and y = 3 x . 1. Solve the equation for x: 5 2x = 5 6 2. Solve the equation for x: 4 (4x+4) = 1/64 3. Sketch the graph of y = 2 x
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4. Sketch the graphs of y = 2 0.5x and y = 2 1.5x on the same axes. 5.
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5.2 Logarithmic Functions Logarithms of x to the base b y = log b x if and only if x = b y Logarithmic Notation 1. log e x = ln x 2. log 10 x = log x Properties of Logarithms for
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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 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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