1. Use the relation between intensity and electric field

For an electromagnetic wave, $I \propto E^2$ So, $E \propto \sqrt{I}$

2. Intensity at the same distance from a bulb

At a fixed distance $r$, the intensity due to a source of power $P$ is $I = \frac{P}{4\pi r^2}$ Thus, at the same distance, $I \propto P$ Hence, $E \propto \sqrt{P}$

3. Compare the electric fields for 100 W and 60 W bulbs

Let the electric field due to the $100\,\text{W}$ bulb at $3\,\text{m}$ be $E$.

For the $60\,\text{W}$ bulb, let the field be $E_{60}$. Then, $\frac{E_{60}}{E} = \sqrt{\frac{60}{100}} = \sqrt{\frac{3}{5}}$ So, $E_{60} = \sqrt{\frac{3}{5}}\,E$

4. Match with the given form

Given, $E_{60} = \sqrt{\frac{x}{5}}\,E$ Comparing, $\sqrt{\frac{x}{5}} = \sqrt{\frac{3}{5}}$ Therefore, $x = 3$

5. Final answer

$\boxed{3}$