Write the expression below as a single logarithm. Please show all of your work.

Question

ln((x^2 – 1)/(x^2 – 6x + 8)) – ln((x+1)/(x+2))

Answer 1

ln((x^2 – 1)/(x^2 – 6x + 8)) – ln((x+1)/(x+2))

when you subtract the logs, you divide the arguments

ln (x+1)(x-1) / [(x+1)(x-1)((x-4)(x-2)]

ln 1/[(x-4)(x-2)]

ln [ (x-4)(x-2) ]^-1

-ln [ (x-4)(x-2)]

Answer 2

6logb v+2logb t

Answer 3

12logb^2vt