How do you find the Limit of #ln(1+5x) - ln(3+4x)# as x approaches infinity? Calculus Limits Determining Limits Algebraically 1 Answer Cesareo R. Jun 16, 2016 #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)# Answer link Related questions How do you find the limit #lim_(x->5)(x^2-6x+5)/(x^2-25)# ? How do you find the limit #lim_(x->3^+)|3-x|/(x^2-2x-3)# ? How do you find the limit #lim_(x->4)(x^3-64)/(x^2-8x+16)# ? How do you find the limit #lim_(x->2)(x^2+x-6)/(x-2)# ? How do you find the limit #lim_(x->-4)(x^2+5x+4)/(x^2+3x-4)# ? How do you find the limit #lim_(t->-3)(t^2-9)/(2t^2+7t+3)# ? How do you find the limit #lim_(h->0)((4+h)^2-16)/h# ? How do you find the limit #lim_(h->0)((2+h)^3-8)/h# ? How do you find the limit #lim_(x->9)(9-x)/(3-sqrt(x))# ? How do you find the limit #lim_(h->0)(sqrt(1+h)-1)/h# ? See all questions in Determining Limits Algebraically Impact of this question 2082 views around the world You can reuse this answer Creative Commons License