How do you find the Limit of #ln (x)/ln (3x) # as x approaches infinity? Calculus Limits Determining Limits Algebraically 1 Answer Eddie Aug 15, 2016 #1# Explanation: #lim_(x to oo) ln (x)/ln (3x)# #lim_(x to oo) ln (x)/(ln 3 + ln x )# #lim_(x to oo) 1/(ln 3/ (ln x ) + 1 )# #(lim_(x to oo) 1)/(lim_(x to oo) ln 3/ (ln x ) + 1 )# #= 1/1 = 1# as #lim_(x to oo) ln (x) = oo# 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 12225 views around the world You can reuse this answer Creative Commons License