Logarithmic Functions Section 2. Objectives Change Exponential Expressions to Logarithmic Expressions and Logarithmic Expressions to Exponential Expressions.

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Presentation transcript:

Logarithmic Functions Section 2

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

where a > 0 and a ≠ 1 Domain: x > 0

Change to an equivalent logarithmic function

Change to an equivalent exponential function

Find the exact value of the logarithmic expression

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

Find the domain of the logarithmic function

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

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

Solve the logarithmic equation.

Use a logarithm to solve the equation.

Pages (22-56 even) ======================== Pages ( even, 118, 121)