# Find the difference between two numbers using log function

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 = 81Output:-77

Input:a = -3, b = 16Output:-19

Input:a = -3, b = -13Output: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 ( a
^{b}) = b log ( a )

Combine these three properties and write.

log

_{e}( e^{a}/ e^{b})

=> log_{e}( e^{a}) – log_{e}( e^{b}) {using property 1}

= > a log_{e}( e ) – blog_{e}( e ) {using property 2}

= > a – b {using property 3}

Note:eis theEuler numberi.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)