Just to be sure i think i did this right i had to simplify $\displaystyle \ln \frac{x^2 e}{y^3 e^x}$ $\displaystyle = \ln x^2 + \ln e - \ln y^3 + \ln e^x$ $\displaystyle = 2 \ln x + 1 - (3 \ln y + x)$
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Yep, no problem there
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