Express as the logarithm of a single expression. Assume that variables represent positive numbers.logcm + logcn

A. log_cmn
B. log_c(m + n)
C. log_c
D. log_cm ? log_cn

Answer: A

Mathematics

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Solve the problem.A 200 gallon tank is filled with pure water. A salt solution with a concentration of 16 g/gal flows into the tank at a rate of 3 gal/min. The thoroughly mixed solution is drained from the tank at a rate of 3 gal/min.(a) Write an initial value problem for the mass of the salt.(b) Solve the initial value problem.

A. (a) m'(t) = -0.015m + 3200, m(0) = 200 (b) m = 3200e-0.015t + 48 B. (a) m'(t) = 0.015m - 48, m(0) = 16 (b) m = -48e0.015t + 48 C. (a) m'(t) = -0.015m + 48, m(0) = 0 (b) m = -3200e-0.015t + e-0.015 D. (a) m'(t) = -0.015m + 48, m(0) = 0 (b) m = -3200e-0.015t + 3200

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Mathematics