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

It appears there might be a slight ambiguity in the notation of the problem. Based on common mathematical problem structures that lead to solvable algebraic equations, I will assume the equation is $9^{\sqrt{x}} = \sqrt{27^x}$. If the intention was $9 \cdot \sqrt{x}$, the problem becomes significantly more complex and typically requires numerical methods.

Assuming the equation is:

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

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