(a) Using laws of logarithms, write the expression below using sums and/or differences of logarithmic expressions which do not contain the logarithms of products, quotients, or powers.

$\displaystyle \displaystyle \ln \sqrt{ \frac{ (x - 6)^{34} }{ (3 x - 7)^{30} } } =$ help (logarithms)

Hint: $\sqrt{u^2} = |u|$.

(b) Use your answer from part (a) to evaluate the derivative.

$\displaystyle \frac{d}{dx} \left( \displaystyle \ln \sqrt{ \frac{ (x - 6)^{34} }{ (3 x - 7)^{30} } } \right) =$ help (formulas)