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Published byCory Fletcher Modified over 4 years ago

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Logarithmic Functions Section 2

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Objectives Change Exponential Expressions to Logarithmic Expressions and Logarithmic Expressions to Exponential Expressions Evaluate Logarithmic Expressions Determine the Domain of a Logarithmic Function Graph Logarithmic Functions Solve Logarithmic Equations

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where a > 0 and a ≠ 1 Domain: x > 0

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Change to an equivalent logarithmic function

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Change to an equivalent exponential function

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Find the exact value of the logarithmic expression

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Since logarithmic and exponential functions are inverses of each other, Domain of the logarithmic fx. = Range of the exponential fx. = (0, ∞) Range of the logarithmic fx. = Domain of the exponential fx. = (-∞, ∞) The argument of a logarithmic function must be greater than zero

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Find the domain of the logarithmic function

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Properties of the Logarithmic Function f(x) = log a x Domain: Positive reals Range: All reals x-intercept: 1 y-intercept: None y-axis is a vertical asymptote Decreasing if 0 1 Graph contains the points (1, 0), (a, 1), and (1/a, -1) Graph is smooth and continuous, with no corners or gaps

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y = ln x if and only if x = e y (inverse functions) ======================== y = log x if and only if x = 10 y (inverse functions)

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Solve the logarithmic equation.

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Use a logarithm to solve the equation.

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Pages 515-516 (22-56 even) ======================== Pages 517-518 (76-110 even, 118, 121)

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