Thread: approximate log(1-x)

Can I approximate log(1-x) with -x, if my ?

If i have an optimization problem: maximize A*x + B*log(1-x)
can I exchange with a problem: maximize A*x + B*(-x) ?

I don't think you could, have you graphed both functions? This should give you a better understanding.

It was a typo. I meant -x.

I plotted both functions and they look very similar for x<0.5

Why can't you just find as part of the overall derivative?

What does that tell me?

Originally Posted by robustor

Can I approximate log(1-x) with -x, if my ?

If i have an optimization problem: maximize A*x + B*log(1-x)
can I exchange with a problem: maximize A*x + B*(-x) ?

I suggest you use a truncated version of the MacLaurin Series which is convergent when .

So theoretically, yes you could truncate it after the first term, but it won't be very accurate. I would suggest truncating it after three or four terms.

For small positive values of x, lets say x<=0.5, or x<=0.25 can I approximate x^2 and x^3 with some function of x?

The reason why I ask is that I cannot have x to the power of something in my objective function

Originally Posted by robustor

For small positive values of x, lets say x<=0.5, or x<=0.25 can I approximate x^2 and x^3 with some function of x?

The reason why I ask is that I cannot have x to the power of something in my objective function

Prove it has given you the series of expansion. For increasing powers of x will get smaller so you can simply say high powers are roughly 0 compared to low powers and discard the former.
At which value of x this applies depends on how accurate your function needs to be.

Sure, i understand that.

My values of x are 0<x<0.25

I can then approximate:

My question was, can I approximate it with something like:

, where f(x) is a linear function of x that is smaller than ?