Question

what properties or rules are used to arrive at this answer?

1/2ln(2x-1)-2ln(x+1)
=
ln((2x-1)^1/2/(x+1)^2)

thanks

Answer 1

two log rules:

log (A^n) = n logA
log(A/B) = logA - logB

your last line has mismatched brackets, should be
ln( (2x-1)^(1/2) / (x+1)^2) )

you can always check: then number of "(" brackets must be the same
as the number of ")" brackets in your expression or equation

Answer 2

thank you for all your help today