calculus - Prove: $lim_{xrightarrow infty} left (frac{x+log 9}{x-log 9} right )^{x}=81$

Over the real line, prove that

$\lim_{x\rightarrow \infty} \left (\frac{x+\log 9}{x-\log 9} \right )^{x}=81$

I've tried L Hospital Rule, which gets too complicated and I'm trying by Squeeze theorem now.

Answer

Hint:

$$\frac{x+a}{x-a}=1+\frac{2a}{x-a}$$