使用对数函数查找两个数字之间的差异

给定两个整数a和b ，任务是使用 log函数找到a和b的减法，即(ab) 。

Note: We can not use the – operator.

例子：

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

Input: a = -3, b = 16  
Output:  -19

Input: a = -3, b = -13  
Output: 10

方法：写这个问题的解决方案，使用日志的以下三个属性

• log( a / b) = log( a ) – log( b )
• log _a( a )  = 1
• log ( a^b ) = b log ( a )

结合这三个属性并编写。

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: e is the Euler number i.e, 2.71828 

请按照以下步骤解决问题：

• ab的减法将是log(exp(a) / exp(b))作为答案。

下面是上述方法的实现。

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

        // 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
    

输出

-22

时间复杂度： O(1)
辅助空间： O(1)