Question

Use the properties of logarithms to expand the logarithmic function

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

Would this be the correct answer?
ln[x^3-x^2+x-1]
I can't seem to expand it any further than that.

Answer 1

your expansion is 100% correct

Answer 2

you can just say
lnx^3-lnx^2+lnx-ln1
lnx^3-lnx^2+lnx-0
which is
lnx^3-lnx^2+lnx

Answer 3

no, you cannot.

ln(x) + ln(y) = ln(xy)

ln(x+y) is NOT ln(x) + ln(y)

instead of expanding the polynomial, you could do

ln[(x^2+1)(x-1)]
= ln(x^2+1) + ln(x-1)