Solve the equation 9 sqrt(x) = sqrt(27^x) for x.

To find the value of $x$, we need to solve the given equation:

$$9\sqrt{x} = \sqrt{27^x}$$

Step 1: Rewrite the numbers 9 and 27 as powers of 3, and express the square roots as fractional exponents.
We know that $9 = 3^2$ and $27 = 3^3$.
Also, $\sqrt{x} = x^{1/2}$ and $\sqrt{27^x} = (27^x)^{1/2}$.

Substitute these into the equation:

$$$$