Simplify the given expression:

${\mathrm{e}}^{x\ln a}$

Find the value of the given expression.

${\log }_{3}8$

Find the value of the given expression.

${\log }_{6}24$

Find the value of the given expression.

${\log }_{5}8$

Find the value of the given expression.

${\log }_{3}30$

Find the value of the given expression.

${\log }_7\frac{1}{4}$

Find the value of the given expression.

${\log }_2\frac{3}{5}$

If ${\log }_{x}3=r$ and ${\log }_{x}6=s$, write the given expression in terms of $r$ and $s$:

${\log }_{3}6$