Use the Laws of Logarithms to expand the expression ln6x2x

Use the Laws of Logarithms to expand the expression.

ln((6x^2)/((x + 4)^2))

Solution

ln((6x^2)/((x + 4)^2))

Use the laws of logarithms :

ln(A/B) = ln(A) - ln(B) ; ln(A^x) = x*lnA ; ln(A*B) = lnA + lnB

ln((6x^2)/((x + 4)^2))

= ln6x^2 - ln(x+4)^2

= lnx^2 + ln6 - 2ln(x+4)

= 2lnx +ln6 - 2ln(x+4)