If $\log_x 2 = 1.2a$ and $\log_x 3 = 1.5a$, find $\log_x \sqrt{12}$ .

$\begin{align}
\log_x \sqrt{12} & = \log_x 12^{0.5} \\
& = 0.5 \log_x 12 \\
& = 0.5 \log_x (4 \times 3) \\
& = 0.5 \log_x 4 + 0.5 \log_x 3 \\
& = 0.5 \log_x 2^2 + 0.5 \log_x 3 \\
& = 0.5(2) \log_x 2 + 0.5 \log_x 3 \\
& = \log_x 2 + 0.5 \log_x 3 \\
& = 1.2a + 0.5(1.5a) \\
& = 1.95a
\end{align}$