with solution

A. True or False. Write true if the statement is correct. Otherwise, write false and give a counterexample. 1. log(x + y) = log x + logy 3. In () = Inx + Iny - Inz 2. log4 () =2 -log4 y 4. (In x) (Iny) = In(x + y) B. Expand each logarithm as much as possible. Write each expression as a sum or difference of logarithms. 6abc mid-n 1. logs af 3. In m-nz 5n2m2-5n2 2. In 30xy 77wz 4. log 10n2m2-10n2m-20n2 C. How does the decibel scale (8) change when the intensity of the sound is: 1. Halved? 2. Tripled? D. Approximate the following logarithms given that log 2 = 0.3010, log 3 = 0.4771, log 5 = 0.6990, and log 7 = 0.8451. 1. log 210 3. log 2. log 4. log E 1500.(b) and (d) items are graded. 1. Describe how the graph of g is obtained from the graph of f. a) f(x) = log2 x, g(x) = 3 + 10g2 -x b) f (x) = Inx, g(x) = - In(x +2) 2. Given the transformation applied to the graph of f (x), write a formula for the resulting function g. a) The graph of f (x) = log x is shifted 5 units to the left and 2 units down. b) The graph of f (x) = log3 x is reflected across the x-axis and shifted 2 units up. c) The graph of f (x) = In x is vertically stretched by a factor of 3. d) The graph of f (x) = log2 x is vertically compressed by a factor of = and reflected across the y -axis