log() function in C++

Log() function in C++ : The log() function in C++ returns the natural logarithm (base-e logarithm) of the argument passed in the parameter.

Syntax for returning natural logarithm: result = log(x) 

Syntax for returning logarithm (base-10 logarithm) of the argument. result = log10(x)

The parameters can be of any data type like int, double or float or long double. Log() function returns value according to the following conditions are as follows:

a) if x>1 then positive ..
b) if 0<x<1 returns a negative value ..
c) if x=1 then it returns 0 ..
d) if x=0 then it returns -inf ..
e) if x<0 then it returns NaN(not a number) 

CPP

// CPP program to implement log() function
#include <bits/stdc++.h>
using namespace std;

// function to evaluate natural logarithm base-e
double valueE(double d)
{
    return log(d);
}

// function to evaluate logarithm base-10
double value10(double d)
{
    return log10(d);
}

// driver program to test the above function
int main()
{
    double d = 10;
    cout << "The logarithm value(base-e) of " << d
        << " is " << valueE(d) << endl;
    cout << "The logarithm value(base-10) of " << d
        << " is " << value10(d) << endl;
    return 0;
}

Output

The logarithm value(base-e) of 10 is 2.30259
The logarithm value(base-10) of 10 is 1

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

Application: One of the applications of log() function is to calculate values related to log, for e.g. while finding polite number we need the formula to be written in code, for that we can use log() function. Given below is an implementation of log() function. 

CPP

// CPP program to find Nth polite number

#include<bits/stdc++.h>

using namespace std;

// function to evaluate n-th polite number
double polite(double n)
{
    n += 1;
    double base = 2;
    return n + (log((n + (log(n) / log(base))))) / log(base);
}

// driver code
int main()
{
    double n = 7;
    cout<< (int)polite(n);
    return 0;
}

Output

11

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

Errors and Exceptions:

• If the input is very large then the result will be inf which stands for infinity.
• If the input is negative then the error will be nan.

Here is the demonstration through example:-

C++

// CPP program to implement log() function
#include <bits/stdc++.h>
using namespace std;

// function to evaluate natural logarithm base-e
double valueE(double d)
{
    return log(d);
}

// function to evaluate logarithm base-10
double value10(double d)
{
    return log10(d);
}

// driver program to test the above function
int main()
{
    double d = -2;
    cout << "Here is the error for input -2 is " << valueE(d)<<endl;
    cout << "Here is the error for input -2 is " << value10(d)<<endl;
    return 0;
}

Output

Here is the error for input -2 is nan
Here is the error for input -2 is nan

Here the error is nan.

C++

// CPP program to implement log() function
#include <bits/stdc++.h>
using namespace std;

// function to evaluate natural logarithm base-e
double valueE(double d)
{
    return log(d);
}

// function to evaluate logarithm base-10
double value10(double d)
{
    return log10(d);
}

// driver program to test the above function
int main()
{
    double d = 1e1000;
    cout << "Here is the error for input 1e1000 is " << valueE(d)<<endl;
    cout << "Here is the error for input 1e1000 is " << value10(d)<<endl;
    return 0;
}

Output

Here is the error for input 1e1000 is inf
Here is the error for input 1e1000 is inf

Here the error is inf.