I want to determine whether the sequence {ln(n) / ln(4n)} converges or not. When finding the limit as n approaches infinity, I have used logarithmic rules to make the sequence ln(n) / [ln(n) + ln(4)], but past this, I do not understand what to do. Why can I not cancel the ln(n) out, as it is in both the numerator in denominator? And if I cannot cancel them out, does the sequence still approach infinity / infinity? I know that the final answer is one, but how do I get to it?