(a) Write

\(3+2\lg a-\frac12\lg(4b^2),\)

where \(a\) and \(b\) are both positive, as a single logarithm to base 10. Give your answer in its simplest form.

(b) Given that \(2\log_c3=7+4\log_3c\), find the possible values of the positive constant \(c\), giving your answers in exact form.