Find the point(s) of intersection of $f(x)$ and $g(x)$ using graphical approximation methods.:
Use graphical approximation methods to find the point(s) of intersection of $f(x)$ and $g(x)$.
\[
f(x)=(\ln x)^{2} ; g(x)=5 x
\]
Answer
Note: The logarithm function is undefined for x ≤ 0, so any solutions must be x > 0.
Step 1 ：Set the two functions equal to each other and solve for x: \((\ln x)^2 = 5x\)
Step 2 ：This equation is not easily solvable algebraically, so we will use a graphical approximation method.
Step 3 ：Graph the two functions \((\ln x)^2\) and \(5x\) on the same set of axes.
Step 4 ：Look for the points where the two graphs intersect. These points are the solutions to the equation.
Step 5 ：Check your solutions by substituting them back into the original equation to ensure they satisfy both functions.
Step 6 ：Note: The logarithm function is undefined for x ≤ 0, so any solutions must be x > 0.
