The functions \(f(x)\) and \(g(x)\) are defined as follows for \(x\gt -\frac23\) by

\(f(x)=x^2+1, \qquad g(x)=\ln(3x+2).\)

(a) Find \(fg(x)\).

(b) Solve the equation \(fg(x)=5\), giving your answer in exact form.

(c) Solve the equation \(gg(x)=1\).