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Find the difference between two numbers using log function

  • Last Updated : 25 Nov, 2021

Given two integers a and b, the task is to find the subtraction of a and b i.e, (a-b) using the log function.

Note: We can not use the operator.

Examples:

Input: a = 4, b = 81
Output: -77

Input: a = -3, b = 16  
Output:  -19

Input: a = -3, b = -13  
Output: 10

Approach: To write the solution to this question, use the following three properties of the log

  • log( a / b) = log( a ) – log( b )
  • log a( a )  = 1
  • log ( ab ) = b log ( a )

Combine these three properties and write.

loge ( ea / eb )
=> loge ( ea )  – loge ( eb )  {using property 1}
= >  a loge ( e )  – bloge ( e )  {using property 2}
= > a – b {using property 3}

Note: e is the Euler number i.e, 2.71828 

Follow the steps below to solve the problem:

  • The subtraction of a-b will be log(exp(a) / exp(b)) as the answer.

Below is the implementation of the above approach.

C++




// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the subtraction
// of two number a and b i.e, (a-b)
int subtract(int a, int b)
{
    return log(exp(a) / exp(b));
}
 
// Driver Code
int main()
{
    int a = -15;
    int b = 7;
 
    cout << subtract(a, b);
 
    return 0;
}

Java




// Java program for the above approach
class GFG {
 
    // Function to find the subtraction
    // of two number a and b i.e, (a-b)
    static int subtract(int a, int b) {
        return (int) Math.log(Math.exp(a) / Math.exp(b));
    }
 
    // Driver Code
    public static void main(String[] args) {
        int a = -15;
        int b = 7;
 
        System.out.print(subtract(a, b));
 
    }
}
 
// This code is contributed by shikhasingrajput

Python3




# Python3 program for the above approach
import math
 
# Function to find the subtraction
# of two number a and b i.e, (a-b)
def subtract(a, b) :
    return math.log(math.exp(a) / math.exp(b));
 
# Driver Code
if __name__ == "__main__" :
 
    a = -15;
    b = 7;
 
    print(subtract(a, b));
     
    # This code is contributed by AnkThon

C#




// C# program for the above approach
using System;
 
public class GFG {
 
    // Function to find the subtraction
    // of two number a and b i.e, (a-b)
    static int subtract(int a, int b)
    {
        return (int)Math.Log(Math.Exp(a) / Math.Exp(b));
    }
 
    // Driver Code
    public static void Main(string[] args) {
        int a = -15;
        int b = 7;
 
        Console.Write(subtract(a, b));
    }
}
 
// This code is contributed by AnkThon

Javascript




<script>
        // JavaScript Program to implement
        // the above approach
 
 
        // Function to find the subtraction
        // of two number a and b i.e, (a-b)
        function subtract(a, b) {
            return Math.log(Math.exp(a) / Math.exp(b));
        }
 
        // Driver Code
 
        let a = -15;
        let b = 7;
 
        document.write(subtract(a, b));
 
    // This code is contributed by Potta Lokesh
    </script>

 
 

Output
-22

 

Time Complexity: O(1)
Auxiliary Space: O(1)

 


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