Example  SEQ.E.2.  Suppose $5*2^{4x}= 20$. Find $x$.
Solution: Since $b=2, k=4, A= 5$, the equation can be solved with $x =\frac 1k \log_2 \frac C A$  where $C = 20$. So the solution is $x =\frac 14 \log_2( \frac {20} 5) = \frac 14 \log_2 (4)=\frac 14 2 = \frac 12.$

Comment: We can consider the expression on the left hand side of the equation as a function of $x$ giving $f(x) = 5*2^{4x}$ . Now the problem can be restated: to find a $x$ where $f(x) = 20$. This problem and its solution can be visualized both on the graph and the mapping diagram for the function $f$.

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 $f(x) = 20$ and the corresponding point on the graph of $f$  will move to the position where the graph of $f$ crosses the line $y = 20$.
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 $C$.