\begin{aligned}
&\textbf{Logarithms}\\[6pt]
&\text{Given that}\\[4pt]
&\log_{10}2=a
\qquad\text{and}\qquad
\log_{10}3=b,\\[10pt]
&\text{Without using a calculator, express each}\\
&\text{of the following in terms of }a\text{ and }b.\\[10pt]
&\text{(a)}\quad \log_{10}12\\[8pt]
&\text{(b)}\quad
\log_{10}\left(\frac{27}{20}\right)\\[8pt]
&\text{(c)}\quad
\log_{10}\sqrt{24}\\[8pt]
&\text{(d)}\quad
\log_{10}\left(\frac{72^2}{5\sqrt{3}}\right)
\end{aligned}