Find most significant bit of a number X in base Y

Given two positive integers X and Y, the task is to find the MSB of X, in the given base Y.
Examples:

Input: X = 55, Y = 3 
Output: 2 
Explanation: 
55 is 2001 in base 3 with first digit as 2.
Input: X = 123, Y = 10 
Output: 1 
Explanation: 
123 is 123 in base 10 with first digit 1. 

Approach: Let the task to find 1st digit of X = 1234 in base Y = 10, So to get First digit = 1:  

Divide 1234 by 1000 
= X / 10³ 
= X / 10^{Number of Digits in X - 1} 
= X / 10^{log(X) / log(10)} (which is for base 10)  

For any other base, we can replace 10 with Y. Therefore, we can calculate the first digit of a number X in base Y by using the formula:

X / Y^{(log(X)/log(Y))}

Below is the implementation of the above approach:  

2

Time Complexity: O(1)

Auxiliary Space: O(1)