MATH 190 Midterm: MATH 190 Louisville Practice Exam 2 160225 Solution
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Practice exam #2 solutions: (10 points) answer the following questions concerning logarithms. (a) (4 points) find the domain of the function f (x) = There are in fact three restrictions on this function: rst, the parameter of the square root must be non-negative, second, the parameter of the logarithm must be positive, and third, the denominator of the fraction must be nonzero. Thus, we require that x 0, 5 x > 0, and log(5 x) = 0. The rst and last requirements are easily simpli ed to 0 x < 5. The last requirement is that 5 x = 1 so x = 4. Thus, our domain is 0 x < 5 with x = 4, or, in interval form, [0, 4) (4, 5). (b) (2 points) determine the value of log2 14 2 log2 6 + log2. 7 . log2 14 2 log2 6 + log2.
