Geometric definition of logarithm (finite and non-kinematic)

Question

Is there a geometric definition of the logarithm function that is non-kinematic and does not involve an infinite procedure?

With base 10, for example. I'm asking for definition, not construction method.

(Napier's 1619 definition was kinematic in nature, as described in this post:

Motivation for Napier's Logarithms).

Answer 1

If you have a exponential equation and plot the function on a 2D surface, Let, $y=f(x)=b^x$

Then,if you plot the inverse function of the above equation $f^{-1}(x)$,then you get a curve,that curve describe the logarithm.