Growth rate of $1/(\mathrm{log}(x)-\mathrm{log}(x-1))$

Let $x>1$ be a real number. Let $y={\displaystyle \frac{1}{\mathrm{log}(x)-\mathrm{log}(x-1)}}$

My question: Approximately how fast does $y$ grow (asymptotically) in terms of $x$? (e.g. linear, polynomial, exponential)?

Let $x>1$ be a real number. Let $y={\displaystyle \frac{1}{\mathrm{log}(x)-\mathrm{log}(x-1)}}$

My question: Approximately how fast does $y$ grow (asymptotically) in terms of $x$? (e.g. linear, polynomial, exponential)?