Answer
$\frac{dy}{dx}=\frac{1}{\ln{5}}\frac{3}{3x-7}$
Work Step by Step
$y=\log_{5}{({3x-7})}=\frac{\ln{({3x-7})}}{ln5}$
On differentiating both sides:
$\frac{dy}{dx}=\frac{1}{ln{5}}\frac{d(\ln{({3x-7})})}{dx}$
$\frac{dy}{dx}=\frac{1}{\ln{5}}\frac{1}{(3x-7)}\frac{d(3x-7)}
{dx}$
$\frac{dy}{dx}=\frac{1}{\ln{5}}\frac{3}{3x-7}$
