4.3 – Logarithmic functions

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Presentation transcript:

4.3 – Logarithmic functions Target Goals: Use the relationship between exponential and logarithmic functions to change them into the opposite form Evaluate logarithms with and without a calculator. Solve logarithmic equations

Exponential vs. Logarithmic form Exponential Form Logarithmic Form

Ex 1) Change each exponential expression to an equivalent expression involving a logarithm:

Ex 2) Change each logarithmic expression to an equivalent expression involving an exponent:

Ex 3) Find the exact value of each:

Domain and Range of Log functions! Domain of a logarithmic function = range of the exponential function = (0,∞) Range of a logarithmic function = domain of the exponential function = (-∞, ∞) Ex 4) Find the domain of each logarithmic function:

Properties of a Logarithmic Function: The domain is the set of positive real numbers; the range is all real numbers. The x-intercept of the graph is 1. There is no y-intercept. The y-axis (x = 0) is a vertical asymptote of the graph. A logarithmic function is decreasing if 0 < a < 1 and increasing if a > 1. The graph of f contains the points (1, 0), (a, 1) and (1/a, -1). The graph is smooth and continuous, with no corners or gaps or holes.

Ex 5) Solve the following equations: