A better way to understand logarithms is to start with the original motivation from Napier himself (https://sites.pitt.edu/~super1/lecture/lec44911/005.htm);

Seeing there is nothing (right well-beloved Students of the Mathematics) that is so troublesome to mathematical practice, nor that doth more molest and hinder calculators, than the multiplications, divisions, square and cubical extractions of great numbers, which besides the tedious expense of time are for the most part subject to many slippery errors, I began therefore to consider in my mind by what certain and ready art I might remove those hindrances. And having thought upon many things to this purpose, I found at length some excellent brief rules to be treated of (perhaps) hereafter. But amongst all, none more profitable than this which together with the hard and tedious multiplications, divisions, and extractions of roots, doth also cast away from the work itself even the very numbers themselves that are to be multiplied, divided and resolved into roots, and putteth other numbers in their place which perform as much as they can do, only by addition and subtraction, division by two or division by three.

This is what provides the intuition viz; convert multiplication/division/etc. of large numbers into addition/subtraction of two other smaller numbers. Logarithms as inverse of Exponentiation came much later. Starting with this generally confuses the student since they do not understand the point of it all.

From https://en.wikipedia.org/wiki/History_of_logarithms;

Napier conceived the logarithm as the relationship between two particles moving along a line, one at constant speed and the other at a speed proportional to its distance from a fixed endpoint.

Since the speed is directly proportional to its remaining distance from the fixed endpoint, it therefore is a deceleration, which results in the characteristic "flattening" of the curve.

Further details for understanding the above can be found at Priority, Parallel Discovery, and Pre-eminence: Napier, Burgi and the Early History of the Logarithm Relation (pdf) - http://www.numdam.org/item/RHM_2012__18_2_223_0.pdf

Everything is logarithms