In an attempt to understand logarithms better for an unrelated problem, I stumbled across the value of $\log_{9}(1000)$ is equal to approximately 3.143. I thought this was interesting, so tried to get a result closer to pi.
The closest I could get from playing around with a calculator is the log base (9+1/70) of 1000:
$\log_{9.014285714285714}(1000)=3.141587$.
I think it is quite interesting that you can get a reasonable (within a few digits) approximation of pi this way, but am posting this here to ask if this is merely a coincidence, since it feels as if I am forcing the result slightly.
Any insight would be appreciated!