Find Cube root of a number using Log function

Given the number N, the task is to find the cube root using the log function.
Examples:

Input: N = 8 
Output: 2.000000
Input: N = 27 
Output: 3.000000 
 

Approach: To solve the problem mentioned above we will use log() function, according to the following formula:

Let cube root of N be d. 
=> ?N = d 
=> N^(1/3) = d 
Now, apply log on both sides: 
log₃ (N^(1/3)) = log₃ (d) 
=> log₃ (d) = 1/3 * log₃ (N) 
=> d = 3^{(1/3 * log₃ (N))} 
 

Below is the implementation of the above problem: 

2.00 

Time complexity: O(log₂(log₃n))
Auxiliary space: O(1)