C++ program to calculate the logarithm of a given number based on a given base

In almost all modern programming languages, we can find some logarithmic functions such as natural logarithm, base 2 logarithm, base 10 logarithm, etc. But sometimes we need to calculate logarithms of different bases that are not in the given library functions. To achieve this we can use a simple logarithmic formula. In this article, we will see how to calculate logarithmic value in C using a given number and a given base.

Formula for calculating logarithm given base

Suppose we have taken a number x, its base is k, which has also been given. The formula is as follows: The translation of follow −

is: follow −

$$\mathrm{log_{k}\left ( x \right )=\frac{log_{m}\left ( x \right )}{log_{m}\left ( k \right )}}$ $

where m is any known (available base)

Use log10(), where m = 10.

C The cmath library provides the log10() method for finding the base 10 logarithm of a given number. us The same function can be used to calculate the logarithm of a given base k. The syntax used is: An example of log10() is as follows −

grammar

#include < cmath >
Log10( <number> )

algorithm

• Read two numbers x and k

• res := (use log10(x) to find the base 10 logarithm of x) / (use log10(k) to find the base 10 logarithm of k)

• return res

Example

#include <iostream>
#include <cmath>
using namespace std;
float solve( int x, int k){
   float answer;
   answer = log10( x ) / log10( k );
   return answer;
}
int main(){
   cout << "Log base 8 for input x = 512 is: " << solve( 512, 8 ) <<
       endl;
   cout << "Log base 9 for input x = 59049 is: " << solve( 59049, 9 )
       << endl;
   cout << "Log base 2 for input x = 1024 is: " << solve( 1024, 2 ) <<
       endl;
   cout << "Log base 4 for input x = 256 is: " << solve( 256, 4 ) <<
       endl;
}

Output

Log base 8 for input x = 512 is: 3
Log base 9 for input x = 59049 is: 5
Log base 2 for input x = 1024 is: 10
Log base 4 for input x = 256 is: 4

Use log2(), where m = 2.

In the cmath library of C, the log2() method allows users to find the logarithm with base 2 given number. The same function can be used to compute the logarithm of a specified base k The following syntax is used to use log2() −

grammar

#include < cmath >
Log2( <number> )

algorithm

• Read two numbers x and k

• res := (use log2( x ) to find the base 2 logarithm of x) / (use log2( k ) to find the base 2 logarithm of x)

• return res

Example

#include <iostream>
#include <cmath>
using namespace std;
float solve( int x, int k){
   float answer;
   answer = log2( x ) / log2( k );
   return answer;
}
int main(){
   cout << "Log base 8 for input x = 512 is: " << solve( 512, 8 ) <<
       endl;
   cout << "Log base 9 for input x = 59049 is: " << solve( 59049, 9 )
       << endl;
   cout << "Log base 2 for input x = 1024 is: " << solve( 1024, 2 ) <<
       endl;
   cout << "Log base 4 for input x = 256 is: " << solve( 256, 4 ) <<
       endl;
}

Output

Log base 8 for input x = 512 is: 3
Log base 9 for input x = 59049 is: 5
Log base 2 for input x = 1024 is: 10
Log base 4 for input x = 256 is: 4

Use log() when m=e.

In the C cmath library, the natural logarithm log() method allows the user to find the logarithm Use base 'e' for the given number. Logarithms can be calculated using a specified base k Same functionality. The following syntax is used to use the log() function −

grammar

#include < cmath >
log( <number> )

algorithm

• Read two numbers x and k

• res := (use log(x) to find the logarithm of x with base e) / (use log(k) to find the logarithm of x with base e)

• return res

Example

#include <iostream>
#include <cmath>
using namespace std;
float solve( int x, int k){
   float answer;
   answer = log( x ) / log( k );
   return answer;
}
int main(){
   cout << "Log base 8 for input x = 512 is: " << solve( 512, 8 ) <<
       endl;
   cout << "Log base 9 for input x = 59049 is: " << solve( 59049, 9 )
       << endl;
   cout << "Log base 2 for input x = 1024 is: " << solve( 1024, 2 ) <<
       endl;
   cout << "Log base 4 for input x = 256 is: " << solve( 256, 4 ) <<
       endl;
}

Output

Log base 8 for input x = 512 is: 3
Log base 9 for input x = 59049 is: 5
Log base 2 for input x = 1024 is: 10
Log base 4 for input x = 256 is: 4

in conclusion

Using the logarithmic formula of a given base can get the logarithmic result, We use any known base logarithm method on a given number x and divide it by The logarithmic base using a known value as the new base as input. In this article we use Three known existing logarithmic functions are log10(), log2() and log() [natural logarithm] Generates results for the given numbers and their given base.

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