Example SEQ.L.2. Suppose $5*\log_2(4x)= 20$. Find $x$.
Solution: Since $b=2, A \ne 0$, the equation can be solved with
$x =2^{\frac C A}$ where $A=5$ and $C = 20$.
So the solution is $ x =\frac14 2^ {\frac {20} 5} =\frac 14 2^4= 4.$
Comment: We can consider the expression on the left hand side of the
equation as a function of $x$ giving $ f(x) = 5*\log_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, $A, k,$, as well as $C$.