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 with the mapping diagram for the function $f$ as the composite of four functions: $R(x) =x-1 ; exp_2 (x) = 2^x; m(x) = 3*x;$ and $s(x)=x+1$.

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 $f(x) = 13$.

Check the box and the diagram will show the solution on the composite mapping diagram by reversing the arrows and that when $s(x) =x+1=13, x=12;$ when $m(x) = 3x = 12, x = 4;$ when $exp_2(x)= 2^x=4, x =2;$ and when $R(x)= x-1 =2; x =3.$

You can use the sliders to investigate other examples by changing the base, $A,h$, and $k$, as well as the point on the final target axis where $C=13$.