1/2[ln(x+1)+2ln(x-1)] +1/3ln x

Question

Condense and write as a logarithm of a single quantity

Answer 1

ln(x^n) = nln(x) and ln(xy) = ln(x) + ln(y)

Using these two facts,

1/2[ln(x+1) + 2ln(x-1)] + 1/3 ln(x) reduces to

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

1/2[ln(x+1)+2ln(x-1)] +1/3ln x