Consider the function f$($x$)=$ln$(5*(1-$x$^(2)))+1.$

$($a$)$ Show using the logarithm rules that

f$($x$)=($log$\_(2)(5)+$log$\_(2)(1-$x$))/($log$\_(2)($e$))+$ln$($e$*($x$+1)).$

I won't attempt to disguise this with a scenario or motivate this exercise beyond the

fact that I really want you to play with logarithm rules a bit!

Hint: Note that $1-$x$^(2)=($x$+1)(1-$x$)$ and that ln$($e$)=1.$

$($b$)$ Determine the domain of f$($x$)$f$($x$)$ in part $($a$)$ since the square complicates thingsx to f$($x$)=(5)/(2).$ Show all your work, and check your answers using

Desmos or some other calculator. $($There is more than $1$ solution, and it's best to use

the original definition$)$