If $\sqrt{5x}\cdot\sqrt{10x}\cdot\sqrt{18x}=30$, find $x$.
We begin by combining the radical expressions on the LHS of the equation, and expressing everything in terms of prime factors \begin{align*} \sqrt{5x}\cdot{\sqrt{10x}}\cdot{\sqrt{18x}}& =30
\\\Rightarrow \qquad \sqrt{5\cdot{x}\cdot{5}\cdot{2}\cdot{x}\cdot{2}\cdot{3^2}\cdot{x}}& =30
\\\Rightarrow \qquad \sqrt{5^2\cdot{2^2}\cdot{3^2}\cdot{x^3}}& =30
\\\Rightarrow \qquad (5\cdot{2}\cdot{3})\sqrt{x^3}& =30
\\\Rightarrow \qquad 30{x^{\frac32}}&=30
\\\Rightarrow\qquad x^{\frac32}&=1
\\\Rightarrow \qquad x&=\boxed{1}
\end{align*}