Python Logarithm Function

Question

I'm looking for an example of operations with logarithms in Python. I've tried with sympy and numpy and I still can't do what I want. For example, for an input like this:

log(x+1)+log(4-x)=log(100) # it's just an example 

the output should give me the x value. I need to do this with any other functions like log(x+1)=4 or log(x)-log(x+1)=log(x).

Is there some method or somewhere (documentation or similar) where can I find how to do this?

Answer 1

I may be misunderstanding what you need to do because you said you tried sympy already. However, it looks like you just want to solve for x in an algebraic equation.

Solving for x in the equation

log(x+1)+log(4-x)=log(100)

using sympy would be

>>> from sympy import Symbol, solve, log
>>> x = Symbol('x')
>>> solve(log(x+1) + log(4-x) - log(100), x)
[3/2 - 5*sqrt(15)*I/2, 3/2 + 5*sqrt(15)*I/2]

If you want, you can check that these two solutions are correct with numpy.

>>> import numpy as np
>>> a = 3/2 - 5*np.sqrt(15)*1j/2
>>> b = 3/2 + 5*np.sqrt(15)*1j/2
>>> np.log(a + 1) + np.log(4-a)
(4.6051701859880918+0j)
>>> np.log(b + 1) + np.log(4-b)
(4.6051701859880918+0j)
>>> np.log(100)
4.6051701859880918

Is that not what you are looking for?

Answer 2

Since log is a non-linear function, you will need to use a non-linear solver like scipy.optimize.fsolve. It take in a function and a guess value and returns the answer in the form of an array. For simplicity reason, I defined the function as a lambda function since we don't need it outside of this line, but creating a function using standard def methods would work as well. The [0] on the back end get the value out of the array to return just the float.

import scipy.optimize
import math

scipy.optimize.fsolve(lambda x: math.log(x+1) - 4, 5)[0] # 5 is guess value
>>> 53.598
# Check
math.exp(4) - 1
>>> 53.598