# ValueError: math domain error

PythonRuntime ErrorLogarithm## Python Problem Overview

I was just testing an example from *Numerical Methods in Engineering with Python*.

```
from numpy import zeros, array
from math import sin, log
from newtonRaphson2 import *
def f(x):
f = zeros(len(x))
f[0] = sin(x[0]) + x[1]**2 + log(x[2]) - 7.0
f[1] = 3.0*x[0] + 2.0**x[1] - x[2]**3 + 1.0
f[2] = x[0] + x[1] + x[2] -5.0
return f
x = array([1.0, 1.0, 1.0])
print newtonRaphson2(f,x)
```

When I run it, it shows the following error:

```
File "example NR2method.py", line 8, in f
f[0] = sin(x[0]) + x[1]**2 + log(x[2]) - 7.0
ValueError: math domain error
```

I have narrowed it down to the log as when I remove log and add a different function, it works. I assume it is because of some sort of interference with the base, I can't figure out how. Can anyone suggest a solution?

## Python Solutions

## Solution 1 - Python

Your code is doing a `log`

of a number that is less than or equal to zero. That's mathematically undefined, so Python's `log`

function raises an exception. Here's an example:

```
>>> from math import log
>>> log(-1)
Traceback (most recent call last):
File "<pyshell#59>", line 1, in <module>
log(-1)
ValueError: math domain error
```

Without knowing what your `newtonRaphson2`

function does, I'm not sure I can guess where the invalid `x[2]`

value is coming from, but hopefully this will lead you on the right track.

## Solution 2 - Python

You may also use `math.log1p`

.

According to the official documentation :

> math.log1p(x)

> Return the natural logarithm of 1+x (base e). The result > is calculated in a way which is accurate for x near zero.

You may convert back to the original value using `math.expm1`

which returns `e`

raised to the power x, minus 1.

## Solution 3 - Python

you are getting math domain error for either one of the reason : either you are trying to use a negative number inside log function or a zero value.

## Solution 4 - Python

You are trying to do a logarithm of something that is not positive.

Logarithms figure out the base after being given a number and the power it was raised to. `log(0)`

means that something raised to the power of `2`

is `0`

. An exponent can never result in `0`

*, which means that `log(0)`

has no answer, thus throwing the `math domain error`

*Note: `0^0`

can result in `0`

, but can also result in `1`

at the same time. This problem is heavily argued over.

## Solution 5 - Python

We face this problem when we use `log()`

or `sqrt()`

from `math`

library. In this problem **“math domain error”**, we are using a negative number like (-1 or another) or a zero number where we should not be use.