# What are the asymptotes of logarithmic functions?

Dec 10, 2017

Asymptote $\to x = 0$

#### 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 ${0}^{\frac{1}{\alpha}} = 10$ and we know that ${0}^{\Omega} = 0$ where $\Omega \in {\mathbb{R}}^{+}$

$\implies$ No value for $\alpha$ and hence $\log 0$ is undifined, and hence an asymptote at $x = 0$