if ln ((x^2 sqrt(x-1)) / (3x-12) = A ln x + B ln (x-1) + C ln (3x-12) then

Question

A= ____________

B= ____________

C= ____________

Answer 1

We would start by expanding the given log into three separate logs using the product and quotient properties of logs and changing square root to 1/2 as an exponent.

ln x² + ln (x - 1)^1/2 - ln (3x-12)

Then we use the power property to move the exponents in front of the ln's.

2ln x +(1/2)ln (x - 1) - ln (3x - 12)

So A = 2

B = 1/2

C = -1