Question

If $lo{g}_2\left(lo{g}_3\right(lo{g}_{4}x\left)\right)=lo{g}_3\left(lo{g}_4\right(lo{g}_{2}y\left)\right)=lo{g}_4\left(lo{g}_2\right(lo{g}_3^2\left)\right)=0$ then x + y + z is

Answer 1

$lo{g}_2\left(lo{g}_3\right(lo{g}_{4}x\left)\right)=0$
$lo{g}_{3}lo{g}_{4}x=1$
$\frac{log\left(lo{g}_{4}x\right)}{log3}=1$
$log\left(lo{g}_{4}x\right)=log3$
$log{4}^x=3\frac{logx}{log4}=3$
$logx=3log4$
$log=log{4}^{3}x=4^3$
Similarly, $y=2^4$
$z=3^2$
$x+y+z=4^3+2^4+3^2$