Logarithmic Functions Section 3.2A Logarithmic Functions Logarithmic functions are functions in which the logarithm of a variable is present. For x > 0, a > 0, and a ≠ 1, y = loga x if and only if x = a y. The function given by f (x) = loga x is called the logarithmic function with base a.

Ex 1: Use the definition of logarithmic function to Ex 1: Use the definition of logarithmic function to evaluate each logarithm at the indicated value of x. a. f (x) = log2 x, x = 32 b. f (x) = log3 x, x = 1 c. f (x) = log4 x, x = 2 d. f (x) = log10 x, x = f (x) = 5 f (x) = 0 f (x) = 0.5 f (x) = -2 Note: log x means log10 x and is called the common logarithm.

Ex 2: Use a calculator to evaluate the function f (x) = log x at each value of x. a. x = 10 b. x = 2.5 c. x = -2 d. x = 0.25 f (x) = 1 f (x) = 0.3979400 Not possible -0.6020600

Properties of Logarithms

Ex 3: Using the properties of logarithms: a. Solve for x: loga x = loga 3 b. Solve for x: log4 4 = x c. Simplify: log5 58 d. Simplify: 7log714 x = 3 x = 1 8 14

Ex 4: On the same coordinate plane, sketch the graph of each function a. f (x) = 2x b. g (x) = log2 x

Suggested Assignment: S 3.2A pg 195 #1 – 34