I am currently going through this paper - "A Subexponential Algorithm for the Discrete Logarithm Problem" by Leonard Adleman.
On page 56, author mentions that Dixon's algorithm - Asymptotically Fast Factorization of Integers, works in $RTIME (O(2^{O{(\log(q)\log\log(q))}^{1/2}}))$ and on page57, mentions that $r_i, s_i$ are smooth with respect to bound $2^{c ({\log(q)\log\log(q)})^{1/2}}$ .
My question is are these logs mentioned in equation, base $e$ or $2$? Because in his paper (on page 255), Dixon has mentioned the complexity equation in $\ln$ which means natural log, i.e. base $e$.