Just as e complements ln, 10 complements log.

Normally, logs are base 10 unless otherwise indicated.

y=log(-log(1-q))

-10^{y}=log(1-q)

10^{-10^{y}}=1-q

q=1-10^{-10^{y}}

q=1-(\frac{1}{10})^{10^{y}}

Please do not double post the same question in two different forums. See: https://www.askmehelpdesk.com/math-sciences/logarithms-513991.html

It is interesting though that Galactus and Unknown008 got the answer in two different forms - though they are eqiuvalent.