Find the value of x in each of the following :

We have,

$2 \sin 3 x=\sqrt{3}$

$\Rightarrow \sin 3 x=\frac{\sqrt{3}}{2}$

Since, $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$

Therefore,

$\sin 3 x=\frac{\sqrt{3}}{2}$

$\Rightarrow 3 x=60^{\circ}$

$\Rightarrow x=\frac{60^{\circ}}{3}$

$\Rightarrow x=20^{\circ}$

Therefore,

$x=20^{\circ}$