It is required to find a root of the function:

$f(x)=xlog(x)-\frac{P}{x}$

Where $P=9$ and $log$ is the natural logarithm $"ln".$

Using MATLAB, use $($a$)$ Newton$-$Raphson and $($b$)$ modified Secant algorithms to solve this equation.

Use a fixed starting point and change the error limit from ${10}^{-4}$ to ${10}^{-14}$ and plot the number of steps to reach the solution with respect to the selected error limit$.$

Select at least $10$ different starting points and plot the number of steps to solve the question with respect distance of the selected starting guess to the root.

$**$NOTE:For both sections, use a single plot for Newton$-$Raphson and modified Secant.