Answer
No solution.
Work Step by Step
Use the quotient rule $\log_b{\dfrac{p}{q}}=\log_b{p} - \log_b{q}$ with $ p=x-4$ and $ q=x+1$ to obtain
$\ln {\dfrac{x-4}{x+1}}=\ln 6$
Simplify to obtain:
$\dfrac{x-4}{x+1}=6$
$ x-4 = 6x+6 \implies x=-2$
But we just reject this solution because we can not take the log of a negative number.
