How do you solve: #lim_(n->oo)(ln(1+e^(2n)))/(ln(1+e^(3n)))# ? Thanks! Calculus Limits Determining Limits Algebraically 1 Answer Cesareo R. Mar 18, 2017 #2/3# Explanation: #(ln(1+e^(2n)))/(ln(1+e^(3n)))=log(e^(2n)(1+e^(-2n)))/log(e^(3n)(1+e^(-3n)))=(log(e^(2n))+log(1+e^(-2n)))/(log(e^(3n))+log(1+e^(-3n)))# so #lim_(n->oo)(ln(1+e^(2n)))/(ln(1+e^(3n)))=lim_(n->oo)(2n+log(1+e^(-2n)))/(3n+log(1+e^(-3n))) = 2/3# 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 2859 views around the world You can reuse this answer Creative Commons License