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I'm trying to show that $$\log_{a}(n) \in \theta(\log_{b}(n))$$ with $a,b > 0$

To prove it, I use the 'limit' theorem :
$$g \in \theta(f) \Leftrightarrow \lim_{n \to +\infty} \frac{g(n)}{f(n)}=c$$ with $c$ real constant. But after that, I get $\log_a$ over $\log_b$ and I don't know how to go on...

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up vote 0 down vote accepted

Use the fact that $(\log_a n)(\log_b a)=\log_b n$. That should help.

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