This isn’t a correct graphical representation of an example of a logarithmic function. It rather resembles a part of an exponential kind of a function, which is in point of fact an inverse version of some logarithmic kind of a function. Moreover, it is not an approach towards (becoming) a constant line (every line is constant by definition, otherwise it would be a curve) that makes logarithms special, but their approach towards a specifically horizontal linear state.

Taking these small yet significant to the article’s main analogy details into account, I’d suggest to the author, Jardena, reviewing the material prior to using it as the background to something as important as the topic of self-awareness is.