Work in progress

When $k = 1$ this equation has the solution $x = b^{ \frac C A}$.

When $k \ne 1$ the equation can be solved so that $x = \frac 1k b^{ \frac C A}$.

Comments: You can move the (red) point labelled x on the left axis of the mapping diagram to a position where the arrow head points to $f(x) = C$ and the corresponding point on the graph of $f$ will move to the position where the graph of $f$ crosses the line $ y = C$.

Check the box and the diagram will show the solution on both the mapping diagram and the graph.

You can use the sliders to investigate other examples by changing the base, $A$, and $k$, as well as $C$.