Log Calculator

A logarithm is the inverse operation of exponentiation. The logarithm of a number `x` to a base `b` is the exponent to which `b` must be raised to produce `x`. This calculator finds that exponent for any valid base and number.

log ( )
Result: 10

How It's Calculated (Change of Base)

Most programming languages only provide functions for the natural log (ln, base *e*) and sometimes the common log (log, base 10). To calculate the logarithm for any base `b`, we use the change of base formula:

logb(x) = logc(x) / logc(b)

Where `c` can be any base. This calculator uses the natural log (ln), so the formula is: `ln(x) / ln(b)`.

Logarithm Rules & Restrictions

  • The base (b) must be positive and not equal to 1.
  • The number (x) must be positive. The logarithm of a negative number or zero is undefined.