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) =?

Question

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

Answer 1

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.

Answer 2

P/Q = A^(-1)BC^4

so

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

answer is b

Answer 3

it's d