Express as a single Logarithm and Simplify:

Question

2/3ln(x^2+1)+1/2ln(x^2-1)-1/2ln(x+1)

Answer 1

ln(x^2+1)^(2/3)+ln((X^2-1)^(1/2)/(x+1)^(1/2)) =

ln(x^2+1)^(2/3)+ ln((x+1)(x-1))^(1/2)/
(x+1)^(1/2)) =
ln(x^2+1)^(2/3)+ln(x-1)^(1/2) =
ln((x^2+1)^(2/3)*(x-1)^(1/2)).

OR ln((crt(x^2+1)^2*sqrt(x-1).