Are there rational $a$ and $b$ with $$a+be = \frac{1}{\ln 2}\ ?$$
This is a special case of Schanuel's conjecture, which I used repeatedly in this answer -- it seems simple enough that it might have an independent proof.
1 of 3
Are there rational $a,b$ with $a+be=1/\ln 2$?
user44143