Write MATLAB Live Script code $(.$mlx file$)$ to estimate $ln(x)$ for a user inputted value of $x$ using the series expansion:

$ln(x)={\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{n}(\frac{x-1}{x}{)}^n=(\frac{x-1}{x})+\frac{1}{2}(\frac{x-1}{x}{)}^2+\frac{1}{3}(\frac{x-1}{x}{)}^3+$dots valid for $x>\frac{1}{2}$

Note: the natural $log$ function in MATLAB is log$.$

Use a for loop to calculate the series. The maximum value of $n$ in the equation above should be a user inputted value of $N($in other words, instead of calculating the infinite series, the user can specify the number of terms so that $n$ goes from $1$ to $N).$

The user should be prompted to enter the value of $x.$ If the value entered is not within the valid range the user should be prompted again for a new value of $x.$

The user should be prompted to enter the value of $N.$

Your code should output the estimated value of $ln(x)$ from the series calculation and the difference between it and the value MATLAB calculates as $log(x).$ Be sure to label what each of the two values are in your output.

Use fprintf statements to have each value display using fixed$-$point notation with a field width of $8$ and $6$ digits after the decimal place. Use $x=1\mathrm{.}5$ and $N=5$ to run your code.

Write a new MATLAB Live Script code $(.$mIx file$)$ to perform the same calculation but this time use a while loop to calculate for as many terms as it takes to have the difference between the series estimate and the actual value of $ln(x)$ to be less than or equal to $0\mathrm{.}00001.$ Also output the number of iterations it took to meet this tolerance. Test your code for $x=1\mathrm{.}5.($Note: you can copy the code from Part $1$ into a new file and edit your code$).$