$1$) $log_2(log_3(log_2x))=1\Leftrightarrow log_3(log_2x)=2$
$\Leftrightarrow log_2x=9\Leftrightarrow x=2^9$
$2$) Đặt $t = \,{\left( {\sqrt {5 + 2\sqrt 6 } } \right)^{{\mathop{\rm sinx}}}}>0$
ta được pt $t+\frac{1}{t}=2$
$\Leftrightarrow t=1\Leftrightarrow sinx=0\Leftrightarrow x = k\pi $
$3)$ $4\sqrt 3 \sin {\rm{x}}\cos x\cos 2x = \sin 8x$
$
\Leftrightarrow \sqrt 3 \sin 4x = 2\sin 4x\cos 4x\\$
$\Leftrightarrow\left[\begin{array}{I}
\sin 4x=0\\\cos 4x=\frac{\sqrt{3}}{2}\end{array}\right.$
$\Leftrightarrow \left[ \begin{array}{l}
x = k\frac{\pi }{4} (k\in Z)\\
x = \pm \frac{\pi }{24} + k\frac{\pi }{2} (k\in Z)
\end{array} \right.
$