# How do you make the graph for #y=ln(1+x/(ln(1-x)))#?

It looks to me like Socratic graphing cannot plot it for some reason.

This is the graph:

And my calculator can plot it also:

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See Socratic graph and explanation.

I hope that , with the interest already shown, Steve could study my

answer and give his comments.

graph{x-(e^y-1)ln(1-x)=0 [-2.5, 2.5, -1.25, 1.25]}

@a-s-adikesavan

I've embedded my comments in the answer rather than as a comment due to all the maths:

For the domain of the function:

Condition 1

Condition 2 I get a different result for the 2nd condition; as follows'

Lets examine the three cases:

Thanks to some help from @jimh we have

Due to the fact that very rapidly we can be dealing with very small numbers with many decimal places, the computer accuracy is a issue when displaying the graph of the function.

Other than looking at derivatives I'm not sure there is much more to add

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To graph ( y = \ln\left(1 + \frac{x}{\ln(1-x)}\right) ), follow these steps:

- Determine the domain of the function, considering any restrictions on the values of ( x ).
- Identify critical points, where the function is undefined or has vertical asymptotes.
- Plot additional points to understand the behavior of the function.
- Sketch the graph, paying attention to asymptotic behavior and any points of interest such as intercepts or extrema.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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