#Import the NumPy library
import numpy as np

#Initiating NumPy array
arr = np.array([[1, 2], [3, 4]])

#Initiating a variable 'log_arr'
log_arr = np.zeros(arr.shape)

#Looping through every element in the 2D array and 
#applying natural Logarithm
for i in range(arr.shape[0]):
    for j in range(arr.shape[1]):
        log_arr[i,j] = np.log(arr[i,j])

#Displays result
print("Logarithmic function:\n", log_arr)