What's the value of $$i^{i^{i^{...}}}$$?
I tried to take log on both sides.
$x=i^x$
$\implies \log x=x \log i$
After this how can I solve this... I am sorry, that I don't know the methods you are explaining... And more over that the question is in school level only..
Such number $x$ statistifies $i^x=x$. This can be solved with Lambert W function. Doing so, gives:
$$x \approx -1.861743075013160441612498412-0.4107999688363923527986399873 i$$ $$x \approx 0.4382829367270321593816295045+0.3605924718713854895879688663 i$$
But we see that they are always positive, so it is the second one.
