(a) Solve \(\lg(x^2-3)=0\).

(b) (i) Show that \(\dfrac{\ln a^{\sin(2x+5)}+\ln\left(\frac1a\right)}{\ln a}\) can be written in the form \(\sin(2x+5)+k\), where \(k\) is an integer.

(ii) Hence find \(\displaystyle\int \dfrac{\ln a^{\sin(2x+5)}+\ln\left(\frac1a\right)}{\ln a}\,dx\).