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.