B2. Let

$$
f(x)=\ln x \quad \text { and } \quad g(x)=\frac{1}{3} x^{3}-x^{2}-6 x+4
$$

be two functions. 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 $q$. Calculate the value of $a$.