Natural logarithm using while loop in Python

Question

The function: y(x) = ln 1/(1-x)

How do I write a Python program to evaluate the above function for any user-specified value of x, where ln is the natural logarithm (logarithm to the base e)? I am to compulsorily use a while loop so that the program repeats the calculation for each legal value of x entered into the program. When an illegal value of "x" is entered, I used break to terminate the program.

I have tried using the following code but it seems not to run appropriately:

import math

n = int(input("Enter the number to be converted: "))

while n >= 0:
    if n <= 0:    
        break

print("Your number is not positive terminating program.") 
    
x = math.log(n) * 1/(1-n)

print("The Log Value is:", x)

Answer 1

Try:

import math

while True: # infinite loop, to be halted by break
    x = float(input('Enter the number to be converted: ')) # get the input
    if x >= 1: # is the input legal?
        print('The function cannot be evaluated at x >= 1.')
        break # break out of the loop if the input is "illegal"
    y = math.log(1 / (1 - x))
    print('The log value is:', y)

1. First, your program might fall into an infinite loop; if you enter n = 1 for example, then n >= 0 is true and n <= 0 is false, so your program runs the while loop indefinitely.

2. A "legal input" to the function must be a (real) number (strictly) less than 1. If n == 1, then you are doing division by zero. If n > 1, then you are entering a negative number into the log function.

In the suggested code, I am checking only the "numerical legality" of the input; i.e., entering an empty string would throw an error. But I think that is beyond what you are asked for in the assignment.