Question

What are the asymptotes of logarithmic functions?

Answer 1

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`