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