/sci/ - Science & Math

Tell me what I'm doing wrong sci:

Let x = 1/y, then log(1+x) = -log(1/(1+x)) = -log(y/(y+1)). Let Y be near 0. The linear approximation for y/(y+1) is y. So,
log(y/(y+1)) [math]\approx[/math] log(y), i.e.
log(1+x) [math]\approx[/math] -log(y) = log(x).

But this should only work when x is small. x is big here since y is small.