How to estimate $\sum_{2 \leq n \leq X} \frac{1}{(\log n)^A} $?

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I was wondering how does one estimate $$ \sum_{2 \leq n \leq X} \frac{1}{(\log n)^A}? $$ where $A>0$. I feel like it should be $\ll \frac{X}{(\log X)^A}$... Any comments would be appreciated. Thank you.