Answer
$y=5x-2$
Work Step by Step
Theorem 5.2 :properties of ln(x),
Theorem 5.3.1:$\ \ \ (\displaystyle \ln x)^{\prime}=\frac{1}{x}$
--------------------
$y=f(x)=3x^{2}-\ln x$
$f^{\prime}(x)=6x-\displaystyle \frac{1}{x}$
The slope of the tangent at ($1,3$) is $f^{\prime}(1)=6-1=5$
Point-slope equation of the tangent line:
$y-y_{0}=m(x-x_{0})$
$y-3=5(x-1)$
$y=5x-5+3$
$y=5x-2$
For (b) and (c), see image attached.
