# Slope of the tangent line

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 $x$.

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

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