I’m learning algorithms from abdul bari videos and I’m confused about something in the context of function comparsion if f(n) = 3n^(√n) and g(n) = 2^((√n)log(n))

i applied log for both functions the first one = log (3n^(√n)) = log(3) + log(n^(√n)) = log(3) + (√n)log(n)
the second function = (√n) log(n)
so first function is greater than the second one but abdul bari solve it with another way and applied log properties on the second function so f(n) remain the same but g(n) will be = 2^(log(n^(√n)))
if we applied another log rule in g(n) it will be = (n^(√n))^(log(2)) and defualt for log base is 2 so g(n) will be = n^(√n) and f(n) = 3n^(√n) now both function asymptoticly are equal

but in my case how should i know that they are both asymptoticly are equal?