Express as a single logarithm:

$2{\log }_a\left(\frac{1}{2}\right)+{\log }_{a}4-{\log }_a\left(\frac{1}{4}\right)$

Express as a single logarithm:

$6\ln x-2\ln (x+1)-3\ln (2x+6)$

Express as a single logarithm:

${\log }_{4}2+3{\log }_{4}3$

Express as a single logarithm:

$\frac{1}{2}{\log }_{7}16+\frac{1}{3}{\log }_{7}x-2{\log }_{7}y$

Given that ${\log }_{a}3=x$and ${\log }_{a}4=y$, write down the following expression in terms of $x$ and $y$.

${\log }_{a}0.25$

Given that ${\log }_{a}3=x$and ${\log }_{a}4=y$, write down the following expression in terms of $x$ and $y$.

${\log }_{a}48$

Given that ${\log }_{a}3=x$and ${\log }_{a}4=y$, write down the following expression in terms of $x$ and $y$.

${\log }_a\left(\frac{1}{12}\right)$

Given that ${\log }_{a}3=x$ and ${\log }_{a}4=y$, write down the following expression in terms of $x$ and $y$.

${\log }_{a}144$

Given that ${\log }_{a}3=x$ and ${\log }_{a}4=y$, write down the following expression in terms of $x$ and $y$.

${\log }_a\left(\frac{27}{16}\right)$