Question

How do you find the Limit of `ln(1+5x) - ln(3+4x)` as x approaches infinity?

Answer 1

`log_e(5/4)`

Explanation:

`f(x)=log_e(1+5x) - log_e(3+4x) = log_e((1+5x)/(3+4x))`

So `lim_{x->oo}f(x) = log_e(lim_{x->oo}(1+5x)/(3+4x)) = log_e(lim_{x->oo}(1/x+5)/(3/x+4)) =log_e(5/4)`