# ValueError: math domain error

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?

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.

From: stackoverflow.com/q/15890503