Example  SEQ.L.3.  Suppose \$3*\log_2(x-1)+1= 10\$. Find \$x\$.
Solution: Since \$b=2, A= 3 \$, the equation can be solved by solving  \$3*\log_2(x-1) = 9 \$ or \$\log_2(x-1)= 3\$. Thus \$x -1 =2^3=8\$ and \$x = 9\$.

Comment: We can consider the expression on the left hand side of the equation as a composite function of \$x\$ giving \$  f(x) = 3*\log_2(x-1)+1\$ . Now the problem can be restated: to find a \$x\$ where \$f(x) = 10\$. 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 ; log_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) = 10\$.
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=10, x=9;\$ when \$m(x) = 3x = 9, x = 3;\$ when \$\log_2(x)= 3, x =2^3=8;\$ and when \$R(x)= x-1 =8; x =9.\$

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=10\$.