# 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:

..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 program to implement log() function #include 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

Application:
One of the applications of log() function is to calculated 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 program to find Nth polite number #include 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

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