Calculate limit for the following function

I want to calculate the limit for the following function.

$$\lim_{n\to+\infty} \frac{(3/2)^n}{(\log n)^{\log n}}$$

I have tried it using L'Hospital use but the result of differentiation is much more complicated.

Answer

Hint:
$$\frac{(3/2)^x}{(\log x)^{\log x}}=e^{x\log(1.5)-\log(x)\log\log(x)}$$