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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 ``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

 ``

Output

`-22`

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

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