Unit 8: Logarithmic Functions (8.4) p.486492 Definition of Logarithm with base b: Let b and y be positive #'s, bâ‰ 1. The logarithm of y with base b denoted by logb y is defined as: logb y = x if and only if bx = y Examples: a) log2 8 = 3 c) log1/2 16 = 4 b) log4 2 = 1/2 d) log7 1 = 0 1 Special Logarithm Values Log of 1 logb 1 = 0 Log of Base b logb b = 1 2 Ex 1: Evaluate the expression a) log4 64 b) log2 32 c) log5 125 d) log16 2 e) log1/3 27 f) log4 .25 3 Logarithm with base 10 is the common logarithm log10 x = log x Logarithm with base e is the natural logarithm loge x = ln x Examples: a) log 7 b) ln .4 4 Inverse Log Functions g(x) = logb x is the inverse of f(x) = bx b = x f(g(x)) = blog x g(f(x)) = logb bx = x 5 Ex 2: simplify a) 10log 5 c) log4 16x 4 b) 4log 7 d) log3 27x 6 Ex 3: Find the inverse of the function a) y = log5 x c) y = ln (x 3) b) y = log x d) y = ln (2x + 4) 7 Graphs of Logarithmic Functions y = logb (x h) + k x = h is a vertical asymptote x > h is the domain, and range is all real numbers if b>1 the graph moves up to the right if 0<b<1 the graph moves down to the right 8 Ex 4: Graph. State the domain and range. a) y = log2 x + 1 b) y = log3 (x 2) 9 HW: p.490491 #1638 even #4872 even #79, 80 10

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