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: -77Input: a = -3, b = 16
Output: -19Input: 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> |
-22
Time Complexity: O(1)
Auxiliary Space: O(1)