The value of $$\lim_{x \to 0}\frac{\log_e\!\left(\sec(ex)\cdot \sec(e^{2}x)\cdots \sec(e^{10}x)\right)}{e^{2}-e^{2\cos x}}$$ is equal to

A

$$\frac{(e^{20}-1)}{2(e^{2}-1)}$$

B

$$\frac{(e^{10}-1}{2(e^{2}-1)}$$

C

$$\frac{(e^{20}-1)}{2e^{2}(e^{2}-1)}$$

D

$$\frac{(e^{10}-1)}{2e^{2}(e^{2}-1)}$$