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Unformatted text preview: Section 7.3: Logarithmic Functions The logarithmic function f x ( 29 = log a x , a ≠ 1 , is the inverse of the exponential function f x ( 29 = a x . The natural logarithmic function f x ( 29 = ln x , (base e), is the inverse of the natural exponential function f x ( 29 = e x . For a 1 , the graph of f x ( 29 = log a x (and also of f x ( 29 = ln x ) is shown below and has the following characteristics: Slowly increasing Vertical asymptote at the y-axis Passes through the point 1,0 ( 29 Domain: 0, ∞ ( 29 Range: -∞ , ∞ ( 29 lim x →∞ log a x = ∞ lim x → + log a x = -∞ Properties of Logarithmic Functions ( x and y are greater than 0 and r is a real number) i) log a xy ( 29 = log a x + log a y ii) log a x y = log a x- log a y iii) log a x ( 29 r = r log a x iv) log a a x ( 29 = x , or ln e x = x v) a log a x = x , or e ln x = x To solve a logarithmic equation (one in which the variable appears in the argument of the log) i) Isolate the log containing the variable.Isolate the log containing the variable....
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