C++ program to calculate the base 10 logarithm of a given value

Natural calculations in a variety of applications require base 10 logarithms. For competitive exams, there are some quick ways to remember some log values. When programming, there are several ways to calculate logarithmic results using library functions as well as some shortcuts. In this article, we will introduce several ways to calculate the base 10 logarithm of a given number in C.

Use log10() function

The library function used to determine the base 10 logarithm of a given argument is called log10(). The response can be an integer or a float. Using this method is very simple; all you have to do is call the function with a single integer argument and the cmath library and let it calculate the base 10 logarithm for you. Let's look at the syntax and related procedures to see how it is used.

grammar

#include < cmath >
log2( <number> )

algorithm

• Take the number x as input
• Use log10(x) to calculate the base 10 logarithm of x
• Return results.

Example

#include <iostream>
#include <cmath>
using namespace std;
float solve( int x ){
   float answer;
   answer = log10( x );
   return answer;
}
int main(){
   cout << "Log base 10 for input x = 100 is: " << solve( 100 ) << endl;
   cout << "Log base 10 for input x = 1000 is: " << solve( 1000 ) << endl;
   cout << "Log base 10 for input x = 5487 is: " << solve( 5487 ) << endl;
   cout << "Log base 10 for input x = 25479 is: " << solve( 25479 ) << endl;
}

Output

Log base 10 for input x = 100 is: 2
Log base 10 for input x = 1000 is: 3
Log base 10 for input x = 5487 is: 3.73934
Log base 10 for input x = 25479 is: 4.40618

Use logarithmic functions with other bases

Some interesting characteristics of logarithms. We can calculate from any base the logarithmic output of another base. To calculate using any logarithmic base, use the following formula.

$$\mathrm{log_{10}\left ( x \right )=\frac{log_{k}\left ( x \right )}{log_{k}\left ( 10 \right )}}$ $

algorithm

• Take the number x as input
• nume := log-base-k ( x )
• deno := log-base-k(10)
• Return (nume/deno).

Example

#include <iostream>
#include <cmath>
using namespace std;
float solve( int x ){
   float nume, deno;
   nume = log( x );
   deno = log( 10 );
   return nume / deno;
}
int main(){
   cout << "Log base 10 for input x = 100 is: " << solve( 100 ) << endl;
   cout << "Log base 10 for input x = 1000 is: " << solve( 1000 ) << endl;
   cout << "Log base 10 for input x = 5487 is: " << solve( 5487 ) << endl;
   cout << "Log base 10 for input x = 25479 is: " << solve( 25479 ) << endl;
}

Output

Log base 10 for input x = 100 is: 2
Log base 10 for input x = 1000 is: 3
Log base 10 for input x = 5487 is: 3.73933
Log base 10 for input x = 25479 is: 4.40618

in conclusion

The log10() method of the cmath package can be used to calculate the base 10 logarithm. The result will be returned as an integer or fraction. Another approach is to use a different logarithmic base and a simple logarithmic formula, as shown in Part II. To obtain more accurate results, we can also use numerical methods to calculate logarithmic results using the bisection method, Newton-Raphson method, or any other nonlinear equation solving technique.

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