# math

posted by
**michelle** on
.

write as a single logarithm:

ln(x/x-1)+ ln(x+1/x)- ln(x^2-1)

please show me the steps.

thanx

Michelle, I hope you know the three main rules of logs.

1. log (AB) = log A + log B

2. log (A/B) = log A - log B

3 log A^n - n log A

Using these rules and guessing at your order of operations you would have

ln[{x/(x-1)}{(x+1)/x}all over (x^2-1)]

factoring the bottom into (x+1)(x-1) and reducing the inside of the square bracket I got

ln(1/(x-1)^2)

now using rule #2 and #3 you would get

ln 1 - ln(x-1)^2

= 0-2ln(x-1)

=-2ln(x-1)

thank u sooooo much. been tryin to figure out wat ive been doing wrong.