h a conclusion, however, disregards a distinguishing feature of logarithmic functions.
But not every phenomenon can be described by an exponential
The distinguishing feature of logarithmic functions is that their rate of growth at a certain moment scales with the value of the function at that moment. A natural logarithmic function is a special case of this in that the scaling is very simple: the rate of growth is at every moment exactly equal to the value of the function at that moment.
Any dataset that can be described in terms of exponentials can also be described in terms of natural exponentials (any exponential function can be transformed such that its base is ), but we have stumbled upon an objective fact about nature (as it comes to us in our observations) whenever we discover that some phenomenon allows a description in terms of exponentials at all.
The fact that we can describe nature in terms of natural logarithms is a consequence of the way we describe nature, but the fact that we can use logarithms at all tells us something about nature’s dynamics.