I need help, If A, B, C, D, E, and F are all positive, P =AB^3 C^5, and Q = A^2 B^2 C, then ln (P/Q) =?

These are the possible solutions...





a. -2 ln A - ln B + 2 ln C





b. - ln A + ln B + 4 ln C





c. - ln A + ln B - ln C





d. -2 ln A - 2 ln B + ln C





e. none of these

I need help, If A, B, C, D, E, and F are all positive, P =AB^3 C^5, and Q = A^2 B^2 C, then ln (P/Q) =?
By exponenet laws we have P/Q = A^(-1)BC^4


Now noting that ln(xy) = ln(x) + ln(y) and ln(x^a) = a*ln(x) we have,


ln(P/Q) = ln(A^(-1)BC^4) = -ln(A) + ln(B) + 4*ln(C)


hence the answer is b.
Reply:it's d
Reply:P/Q = A^(-1)BC^4





so





In(P/Q) = -InA + InB +4InC





answer is b