Numerical Analysis: Roundoff Error. $($a$)$ Show that

$ln(x-\sqrt[\phantom{2}]{x^2-1})=-ln(x+\sqrt[\phantom{2}]{x^2-1})$

$($b$)$ Which of the two formulas is more suitable for numerical computation? Explain your rationale

and provide a numerical example $($complete with code$)$ that highlights the differences in

accuracy.

$($c$)$ What $($if any$)$ precautions should you take to ensure that you have a well$-$defined and robust

algorithm?