Example  SEQ.3.  Suppose \$3*2^{x+1}+1= 13\$. Find \$x\$.
Solution: Since \$b=2, A= 3 \$, the equation can be solved by solving  \$3*2^{x+1}= 12\$ or \$2^{x+1}= 4\$. Thus \$x +1 =2\$ and \$x = 1\$.

Comment: We can consider the expression on the left hand side of the equation as a composite function of \$x\$ giving \$  f(x) = 3*2^{x+1}+1\$ . Now the problem can be restated: to find a \$x\$ where \$f(x) = 13\$. This problem and its solution can be visualized the mapping diagram for the function \$f\$ as the composite of four functions: \$R(x) =x+1 ; exp_2 ; m(x) = 3*x;\$ and \$s(x)=x+1\$.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

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\$.