Question #e9baa Calculus Limits Limits at Infinity and Horizontal Asymptotes 1 Answer Andrea S. Feb 21, 2017 #lim_(x->oo) ln(3x)-ln(2x) = ln (3/2)# Explanation: For any #a,b > 0# we have that: #ln(ax) -ln(bx)# is a constant. Using the properties of logarithms: #y(x) = ln(ax) - ln(bx) = ln ((ax)/(bx)) = ln (a/b)#. Answer link Related questions What kind of functions have horizontal asymptotes? How do you find horizontal asymptotes for #f(x) = arctan(x)# ? How do you find the horizontal asymptote of a curve? How do you find the horizontal asymptote of the graph of #y=(-2x^6+5x+8)/(8x^6+6x+5)# ? How do you find the horizontal asymptote of the graph of #y=(-4x^6+6x+3)/(8x^6+9x+3)# ? How do you find the horizontal asymptote of the graph of y=3x^6-7x+10/8x^5+9x+10? How do you find the horizontal asymptote of the graph of #y=6x^2# ? How can i find horizontal asymptote? How do you find horizontal asymptotes using limits? What are all horizontal asymptotes of the graph #y=(5+2^x)/(1-2^x)# ? See all questions in Limits at Infinity and Horizontal Asymptotes Impact of this question 1389 views around the world You can reuse this answer Creative Commons License