Question

How do you use the graphing calculator to solve \[3x-2={{5}^{x-1}}\]?

Answer 1

Hint: In this problem, we can use a graphing calculator to solve and find the value of x. We can first take a graphing calculator and write both the given equations separately in it. We can then see where the given two equations intersect, the intersection is where they are equal. The intersection point gives the value of x, we can then substitute the value of x in the given equation to check whether it is correct.

Complete step by step solution:
We know that the given equation is,
\[3x-2={{5}^{x-1}}\]
We can now plot the above two terms in the left-hand side and the right-hand side, separately in the graph.
 We can then find the point of intersection where both the equations meet.
We should know that this is where the given two equations are equal.
We can then write the intersection points which is the value of x.

In the above graph, we can see that the intersection is at \[x=1,x=1.71\].
Therefore, the value of \[x=1\text{ and }1.71\].

Note: Students make mistakes while using the graphing calculators, which have tools in them. We can easily graph the given data and find or solve the given problems. We can now substitute the value of x in the given equation to check whether it is correct.
Substitute x = 1 in \[3x-2={{5}^{x-1}}\] we get
\[\begin{align}
  & \Rightarrow 3\left( 1 \right)-2={{5}^{1-1}} \\
 & \Rightarrow 1=1 \\
\end{align}\]
Substitute x = 1.71 in \[3x-2={{5}^{x-1}}\], we get
\[\begin{align}
  & \Rightarrow 3\left( 1.71 \right)-2={{5}^{1.71-1}} \\
 & \Rightarrow 3.13=3.13 \\
\end{align}\]
Therefore, the values are correct.