Solve the following equation for $x$:

${\log }_{4}32=x-4$

Solve the following equation for $x$:

${\log }_7\left(2x^2-1\right)=2$

Solve the following equation for $x$:

$\log \left(x^2-21\right)=2$

Solve that following equation for x :

${\log }_6(x-2)(x+3)=1$

Solve the following equation for $x$:

${\log }_6(x-2)+{\log }_6(x+3)=1$

Solve the following equation for $x$:

$\log (\mathrm{x}+1)+\log (\mathrm{x}-1)=\log 11+2 \log 3$

Solve for x and y :

$\frac{\log x}{3}=\frac{\log {\displaystyle y}}{2}and \log \left(xy\right)=5$