log()

The log() function in PHP returns the logarithm of a number. By default it returns the natural logarithm — the logarithm to base e (Euler's number, approximately 2.71828) — but you can pass a second argument to compute the logarithm to any base.

A logarithm answers the question "to what power must the base be raised to produce this number?" For example, log(8, 2) is 3, because 2 raised to the power of 3 equals 8. This page covers the syntax, common bases, edge-case behavior, and a practical use case.

Syntax

log(float $num, float $base = M_E): float

The function returns a float: the logarithm of $num to the given base.

Basic example: natural logarithm

When you call log() with a single argument, you get the natural logarithm (base e):

Using a custom base

Pass a second argument to compute the logarithm to a different base. This is handy for base-2 (binary) or base-10 (common) logarithms:

<?php
echo log(100, 10), "\n"; // 2  (10^2 = 100)
echo log(8, 2), "\n";    // 3  (2^3 = 8)
echo log(1, 5), "\n";    // 0  (any base^0 = 1)
?>

For base-10 specifically, PHP also offers the dedicated log10() function, and for small values near 1 there is log1p(), which is more accurate than log(1 + x).

Edge cases to watch for

The mathematical logarithm is only defined for positive numbers, so log() returns special float values outside that range:

<?php
echo log(1), "\n";   // 0   — log of 1 is always 0
echo log(0), "\n";   // -INF — log of 0 is negative infinity
echo log(-5), "\n";  // NAN — log of a negative number is "not a number"
?>

Because NAN and INF propagate silently through arithmetic, validate input before calling log():

<?php
$value = -5;

if ($value > 0) {
    echo log($value);
} else {
    echo "log() requires a positive number";
}
// Outputs: log() requires a positive number
?>

You can detect these results with is_nan() and is_infinite() if a value reaches log() unchecked.

A practical use case

Logarithms are common when you need to know how many digits a number has, or to scale data. For example, the number of decimal digits in a positive integer is floor(log10($n)) + 1:

<?php
$n = 12345;
$digits = (int) floor(log10($n)) + 1;

echo "{$n} has {$digits} digits"; // Outputs: 12345 has 5 digits
?>

Related functions

• log10() — base-10 logarithm.
• log1p() — accurate log(1 + x) for small x.
• exp() — the inverse of the natural log (e raised to a power).
• pow() — raise a number to a power.
• sqrt() — square root.
• PHP Math Functions — overview of all math helpers.

Conclusion

The log() function is a reliable tool for logarithmic calculations in PHP. With its optional second argument it handles any base, while its natural-log default covers the most common need. Remember the edge cases — log(0) is -INF and log() of a negative number is NAN — and validate input to keep your calculations robust.

Practice