Noting that (y^(sqrt(x)))^((z/x)sqrtx) = y^z, we just need to work out 10^sqrt(x) and ((100/x)*sqrt(x)), without any larger numbers.
10^100=(10^2)^50 100^50 which is the closest integer variant
10^100=10^(sqrt2)^((100/2)*sqrt2) around 26^71
10^100=(10^(sqrt3))^(100/(3)*sqrt(3)) around 54^58
10^100=(10^(sqrt3.05))^(100/(3.05)*sqrt(3.05)) around 56^57
Using direct evaluation, WolframAlpha gives
10^sqrt(x)=((100/x)*sqrt(x)), x ≈ 3.08205937..., when 10^sqrt(x)≈ 56.9612
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Posted by broll
on 2023-03-28 00:18:18 |
a rough approximation using basic principles
