Perpendicular tangent lines to two functions

Let $$f(x) = \ln x \quad \text{and} \quad g(x) = \frac{1}{3}x^3 - x^2 - 6x + 4,$$ and let $p$ be the tangent to the graph of $f$ at the point $S(a, b)$, and $q$ be the tangent to the graph of $g$ at the point $T(a, c)$. The tangent $p$ is perpendicular to the tangent $q$. Compute the value of $a$.