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Find the slope of the tangent line $(-\frac{7}{2} , 0)$ for $f(x)= \ln\frac{7(x+3)}{x}$.

I've tried taking the derivative of the equation and then setting it equal to one and solving for $x$.

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    $\begingroup$ Is $(-\frac72,0)$ even on the graph of $f$? $\endgroup$ – user714630 Nov 23 '13 at 0:19
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    $\begingroup$ ...and what happened with the derivative?! But, of course, Karl's question is even more basic. $\endgroup$ – DonAntonio Nov 23 '13 at 0:19
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    $\begingroup$ Oh, the whole fraction is the argument to $\ln$. I would like confirmation from the OP that this is the intended expression: $$\ln\left(\frac{7(x+3)}x\right)$$ $\endgroup$ – user714630 Nov 23 '13 at 0:20
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Hints:

$$\log(f(x))=\frac{f'(x)}{f(x)}$$

$$\log\left(\frac{7(x+3)}x\right)=\log 7+\log(x+3)-\log x\;\;\ldots\ldots$$

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