What are the asymptotes of logarithmic functions?

1 Answer
Dec 10, 2017

Answer:

Asymptote # ->x = 0 #

Explanation:

We can sketch the logorithmic fucntion to be able to determine any asymptotes:

graph{log(x) [-2.156, 13.84, -6.344, 1.65]}

Now we can clearly see that the function asymptotes towards #x=0# in other words, it will approach #x=0# but never actaully reach it

Where #log 0 # is like saying, what value of #alpha # does #10^alpha = 0 # But we know that #alpha# has no defined real value, as that like saying #0^(1/alpha) = 10# and we know that #0^Omega = 0 # where #Omega in RR^+ #

#=> # No value for #alpha# and hence #log0 # is undifined, and hence an asymptote at #x=0#