Critical value of the most powerful test for a Pareto-type density

Let $X$ be a random variable of continuous type with probability density function

$$f(x|\theta)=\begin{cases}\dfrac\theta x\left(\dfrac3x\right)^\theta, & x>3,\ 0, & \text{otherwise,}\end{cases}\quad\theta>0.$$

Based on single observation $X$, the most powerful test of size $\alpha=0.1$, for testing $H_0:\theta=1$ against $H_1:\theta=2$, rejects $H_0$ if $X<k$. Then the value of $k$ is