How to Calculate Logarithm Base 2 in C/C without a Built-in Function?

How to Calculate Logarithm Base 2 in C/C Using Mathematical Conversion

In C/C , the built-in logarithm functions are log(), which calculates the natural logarithm (base e), and log10(), which calculates the logarithm base 10. However, sometimes you may need to calculate the logarithm base 2, and they do not directly offer this functionality.

To calculate the logarithm base 2 using simple mathematics, you can convert it to another base and then use the existing log function. The equation for this conversion is:

log<sub>2</sub> (x) = log<sub>y</sub> (x) / log<sub>y</sub> (2)

where y can be any base. Typically, y is either 10 or e, depending on the available log functions in your programming language.

In C/C , you can use the log() function to calculate the logarithm base e and log10() to calculate the logarithm base 10. So, to calculate the logarithm base 2, you can use the following code:

<code class="c">#include <iostream>
#include <cmath>

double log2(double x) {
  return log10(x) / log10(2);
}

int main() {
  double number;
  std::cout << "Enter a number: ";
  std::cin >> number;

  std::cout << "log2(" << number << ") = " << log2(number) << std::endl;

  return 0;
}</code>

This code takes the input number, calculates log base 10 and divides it by log base 2. The result is the logarithm base 2 of the input number.

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