Compute lim_(n-> oo) ln(3n+7) - ln(n)

vagnhestagn

vagnhestagn

Answered question

2022-09-01

Compute lim n ln ( 3 n + 7 ) ln ( n )
The reason why I'm having trouble with this problem is because it involves natural log (ln) and I need to find the limit.
I need to find lim n ln ( 3 n + 7 ) ln ( n )
I noticed that as n approaches infinity, ln ( n ) should be approaching but I'm having trouble finding the limit since ln ( 3 n + 7 ) is in the sequence.

Answer & Explanation

Garrett Valenzuela

Garrett Valenzuela

Beginner2022-09-02Added 9 answers

Hint:
ln ( x ) ln ( y ) = ln ( x y )
Edit:
ln ( 3 n + 7 ) ln ( n ) = ln ( 3 n + 7 n ) = ln ( 3 + 7 n )
If  lim n 7 n = 0 , what remains?

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