Hi,

I'm looking for help in proving $\log_2 n - \log_{10} n \in \Omega(\log_{12} n)$. I'm having a really hard time with determining this, especially since its not a polynomial.

Also, the expansion of $\log_2 n - \log_{10} n \in \Omega(\log_{12} n)$ is $\exists c, n_0 \in \mathbb{R}^+, \forall n \in \mathbb{N}, n \geq n_0 \Rightarrow \log_2 n - \log_{10} n \geq c \cdot \log_{12} n$

I tried playing around logarithm rules, but nothing really came out of that for me.

Please let me know!