jmc

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