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Logarithmic function - definition • The logarithmic function is given by where: x0 and y log b x b 0, b 1 y b x • Example 1: The function y log 3 x is a logarithmic function with base 3, and is equivalent to 3y x . To remember this pattern, just think of moving the base 3 under the “y” and remove the “log.” • Example 2: The function y log 10 x is a logarithmic y function with base 10, and is equivalent to 10 x. Table of Contents Logarithmic function - definition • Example 3: The equation y log 5 x does not represent a logarithmic function, since b = -5 < 0. • The evaluation of a logarithmic expression follows the pattern of the definition. To evaluate log b c think of the equation y log b c , which has the alternate form b y c . Finding the value of y translates into asking the question ... “b raised to what power yields c?” • Example 4: Evaluate the expression log 2 8 Since 2 raised to the 3 power is 8, the answer is 3. Table of Contents Slide 2 Logarithmic function - definition 1 • Example 5: Evaluate the expression log 5 125 1 1 3 Since 5 3 the answer is - 3. 5 125 • Example 6: Evaluate the following expressions: Expression Work Answer log b b ? log b 1 ? b1 b 0 b 1 1 log b b ? bx bx x x Table of Contents 0 Slide 3 Logarithmic function - definition Table of Contents