Answer
$\displaystyle \frac{1}{2}C-2A $
Work Step by Step
$\displaystyle \sqrt{\frac{3}{16}} = (\frac{3}{16})^{1/2}= (\frac{3}{2^{4}})^{1/2}=\frac{3^{1/2}}{2^{2}}$
$\displaystyle \log_{b}\sqrt{\frac{3}{16}}=\log_{b}(\frac{3^{1/2}}{2^{2}})$
...apply the Quotient Rule: $\displaystyle \quad \log_{b}(\frac{M}{N})=\log_{b}\mathrm{M}-\log_{b}\mathrm{N}$
$=\log_{b}3^{1/2}-\log_{b}2^{2}$
...apply the Power Rule: $\quad \log_{b}(M^{p})=p\cdot\log_{b}\mathrm{M}$
$=\displaystyle \frac{1}{2}\log_{b}3-2\log 2$
... use the definitions of A and C
$=\displaystyle \frac{1}{2}C-2A $
