Smallest trial count for an at-least-one threshold

A synthetic procedure is repeated independently for each sample

On each run, the probability of the specified result is \(\frac{1}{5}\), and the probability of another result is \(\frac{4}{5}\). The trials are independent

Let \(X\) be the number of successes in \(n\) independent runs. The required probability threshold is \(0.737\)

Use the relation \(\Pr(X\ge 1)=1-(1-p)^n\) for the probability of at least one success

How many trials are required at minimum for the probability of at least one success to be above 0.737?