Simplify Ln

Here is what they did:

x^-1 = 1/x and y^-1 = 1/y so they made it

ln(1/x - 1/y)

Then they got common denominators and combined the fractions

ln((y - x)/(xy))

Then they used the ln properties (ln a/b = lna - lnb, and ln ab = ln a + ln b)

= ln(y - x) - ln(xy)

= ln (y - x) - (lnx + lny)

= ln (y - x) - ln x - ln y

and apparently that's simpler form than the original...

yes, you are right it should be lny=lnx*ln(1+e^x)