Limit of log with factor Problem If lim_(n->oo} f(n)-log n-log log n = y where f is some function, does this imply that lim_(n->oo} f(n) - log (xn) - log log n = y for some x in O(1)? Or does this give another Limit y? Progress For y=0 or y=+-oo, I think, this factor x should not change anything, but for y in (−oo,0)uu(0,oo), I think this Limit should change, shouldn't it?

malaana5k

malaana5k

Answered question

2022-09-24

Limit of log with factor
Problem
If
lim n f ( n ) log n log log n = y
where f is some function, does this imply that
lim n f ( n ) log ( x n ) log log n = y
for some x O ( 1 )? Or does this give another Limit y?
Progress
For y = 0 or y = ± , I think, this factor x should not change anything, but for y ( , 0 ) ( 0 , ), I think this Limit should change, shouldn't it?

Answer & Explanation

niveaus7s

niveaus7s

Beginner2022-09-25Added 8 answers

Notice that
log ( x n ) = log x + log n
so the limit is the same if y = ± and it becomes y + log x if y R
Raina Gomez

Raina Gomez

Beginner2022-09-26Added 3 answers

Hint:
log ( a b ) = log a + log b

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