math
posted by Austin on .
write the expression as a sinle logarithm. express powers as factors.
In (x/x1)+In(x+1/x)In(x^21)
Please show work.

You MUST put brackets for the denominators to avoid ambiguity
I am sure you mean
ln ( x/(x+1) ) + ln( (x+1)/x )  ln (x^2  1)
then
= lnx  ln(x+1) + (ln(x+1)  lnx  ln( (x+1)(x1)
= lnx  ln(x+1) + ln(x+1) + lnx  ln(x+1)  ln(x1)
=  2ln(x+1)
or
ln [ (x/(x1) ((x+1)/x) / ((x+1)x1))
= ln (1/(x1)^2)
= ln1  ln(x1)^2
= 0  2ln(x1)
= 2ln(x1)