Pandas apply but only for rows where a condition is met

The other answers are excellent, but I thought I'd add one other approach that can be faster in some circumstances – using broadcasting and masking to achieve the same result:

import numpy as np

mask = (z['b'] != 0)
z_valid = z[mask]

z['c'] = 0
z.loc[mask, 'c'] = z_valid['a'] / np.log(z_valid['b'])

Especially with very large dataframes, this approach will generally be faster than solutions based on apply().

You can just use an if statement in a lambda function.

z['c'] = z.apply(lambda row: 0 if row['b'] in (0,1) else row['a'] / math.log(row['b']), axis=1)

I also excluded 1, because log(1) is zero.

Output:

   a  b         c
0  4  6  2.232443
1  5  0  0.000000
2  6  5  3.728010
3  7  0  0.000000
4  8  1  0.000000

Hope this helps. It is easy and readable

df['c']=df['b'].apply(lambda x: 0 if x ==0 else math.log(x))

You can use a lambda with a conditional to return 0 if the input value is 0 and skip the whole where clause:

z['c'] = z.apply(lambda x: math.log(x.b) if x.b > 0 else 0, axis=1)

You also have to assign the results to a new column (z['c']).