On a blank paper there were drawn two perpendicular axes $x$ and $y$ with the same scale. The graph of a function $y=f(x)$ was drawn in this coordinate system. Then the $y$ axis and all the scale marks on the $x$ axis were erased. Provide a way how to draw again the $y$ axis using pencil, ruler and compass: (a) $f(x)= 3^x$; (b) $f(x)= \log_a x$, where $a>1$ is an unknown number.
Problem
Source: 2022 Tournament of towns Spring Senior A-level
Tags: function, analytic geometry, geometry, Ruler, compass