How can custom functions be defined and used in PHP to calculate logarithms, especially if built-in functions like log() are not available?

To calculate logarithms in PHP when built-in functions like log() are not available, you can define a custom function that approximates the logarithm using mathematical formulas. One common method is to use the Taylor series expansion for the natural logarithm function. By implementing this custom function, you can calculate logarithms in PHP without relying on built-in functions.

<?php
// Custom function to calculate natural logarithm using Taylor series expansion
function custom_log($x, $precision = 10) {
    $result = 0;
    for ($n = 1; $n < $precision; $n++) {
        $result += (1 / $n) * pow((($x - 1) / ($x + 1)), (2 * $n - 1));
    }
    return 2 * $result;
}

// Example usage
$num = 5;
$log_value = custom_log($num);
echo "Logarithm of $num is: $log_value";
?>