How do you find the vertical asymptote of a logarithmic function?

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Answer 1 · 2015-10-28T18:12:40

The vertical asymptote is (are) at the zero(s) of the argument and at points where the argument increases without bound (goes to #oo#).

#f(x) = log_b("argument")# has vertical aymptotes at #"argument" = 0#

Example #f(x) =ln(x^2-3x-4).# has vertical asymptotes

#x=4# and #x=-1#

graph{y=ln(x^2-3x-4) [-5.18, 8.87, -4.09, 2.934]}

Example #f(x) =ln(1/x)# has vertical asymptote

#x=0#

graph{ln(1/x) [-5.18, 8.87, -4.09, 2.934]}

Example #f(x) =ln(1/x^2)# alsohas vertical asymptote

#x=0#

graph{ln(1/x^2) [-5.18, 8.87, -4.09, 2.934]}