#Two functions have the same order
limpid pawnBOT
copper dust
Yep, that's the idea
To simplify logarithms, factor polynomials by their dominant term (the x^n with the biggest n) and use log(ab) = log(a)+log(b)
For the factorial, you can use that same property of log (I don't know your definition of x! But maybe you can stick to n! with n integer)
And for polynomials without log, you can just look at the dominant term
That's the correct intuition. What makes you think that ?
copper dust
Yep ! So, between C and D
For C, on one hand we have xlog(x) which is equal to log(x^x). And on the other hand, log(x²+1) which is roughly the same as log(x²) when x is big
(the exercise says x>1, but intuitively it actually asks for the behavior when x goes to +∞ )
What you can say is log(x²) = 2log(x) yes
(which is of order log(x) )
Nope, because log(x²)=2log(x) is of the same order as log(x)