Evaluate the limit using an appropriate substitution.
https://i.gyazo.com/4e72308519ac01411b2404ba5d2f260a.png

Hint: [Hint: t = ln x]

Question

Evaluate the limit using an appropriate substitution.
https://i.gyazo.com/4e72308519ac01411b2404ba5d2f260a.png

Hint: [Hint: t = ln x]

trojanpoem · Answer

$$\lim_{lnx \rightarrow  infty}\frac{ \ln2 + lnx }{ \ln3 + lnx }   $$


$$\lim_{lnx \rightarrow  \infty}\frac{ \ln2/lnx + lnx/lnx }{ \ln3/lnx + lnx/lnx } $$

= 1/1 = 1

anonymous · Answer

how did you get that answer? may you explain the steps?

trojanpoem · Answer

I did as the hint suggested , separate ln x from the coefficient .

lnab = ln a + ln b

meanwhile:

ln2x = ln2 + lnx   , ln3x = ln3 + lnx

let lnx = t

$$\lim_{lnx \rightarrow \ln \infty} = \lim_{t \rightarrow \infty} \frac{ \ln2 + t }{ \ln3 + t }$$

ln2 , ln3 are just normal numbers. solve it like any other infinity limit.