import numpy as np
df["log_2"] = np.log(df["col2"])
print(df)

   col1   col2     log_2
0  1.00    3.0  1.098612
1  1.20   45.5  3.817712
2  0.75   28.0  3.332205
3  1.60  100.0  4.605170

print(df[["col1", "log_2"]].var())

col1     0.128958
log_2    2.262886
dtype: float64