Write the expression as the logarithm of a single quantity.

Question

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

Answer 1

ln 2 + 1/2 ln(x +1)-2 ln(1+ x^(1/2))
= ln2 + ln √(x+1) - ln( 1+√x)^2
= ln [ 2√(x+1)/(1+√x)^2 ]