Mathematics

Mathematics

Problem

Before differentiating implicitly, a student takes the natural logarithm of both sides of the equation x3y2e5y=7x^{3}y^{2}e^{5y}=7. Which of the following equations is obtained after this step? a) 3ln⁡x+2ln⁡y+5ln⁡y=ln⁡73\ln x+2\ln y+5\ln y=\ln 7 b) 3ln⁡x+2ln⁡y+5y=ln⁡73\ln x+2\ln y+5y=\ln 7 c) 3ln⁡x+2ln⁡y+5y=73\ln x+2\ln y+5y=7 d) ln⁡x3+ln⁡y2+5y=ln⁡7\ln x^{3}+\ln y^{2}+5y=\ln 7

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