I'm reading about maximum likelihood [here](http://www.math.utah.edu/~levin/M5080/mle.pdf).

In the last paragraph of the first page, it says:

![enter image description here](https://i.stack.imgur.com/12GBp.png)

Why does the value of $p$ that maximizes $\log L(p;3)$ is the same $p$ that maximizes $L(p;3)$. The fact that it mentions that log is an increasing function does not help me understand it at all. Does this method work for any increasing function?

I've covered single and two variable optimization but have not come across this fact until now. I'd like to understand why it must be true and read more about its explanation. So, I would also appreciate it if someone can provide some links to it (I don't know what term to search).