Logarithm Calculator

Logarithm is the inverse of exponentiation. If b^y = x, then log_b(x) = y. Common logarithm (log) uses base 10, natural logarithm (ln) uses base e (approximately 2.718). Logarithms are used in measuring earthquake intensity, sound levels, and algorithm complexity.

1. 1

   Select Logarithm Type

   Choose base 10 (log), natural (ln), base 2, or custom base

2. 2

   Enter Value

   Input the positive number to calculate its logarithm

3. 3

   Enter Custom Base

   If using custom base, enter a positive value not equal to 1

4. 4

   View Result

   The result displays with the calculation method explained

• 1

  log(1) = 0 for any base (because b^0 = 1)

• 2

  log_b(b) = 1 always (because b^1 = b)

• 3

  log(a x b) = log(a) + log(b)

• 4

  log(a/b) = log(a) - log(b)

• 5

  log(a^n) = n x log(a)

• Calculating logarithm of zero or negative numbers - log is only defined for positive values

• Confusing log and ln - log usually means base 10, ln means base e

• Assuming log(a+b) = log(a) + log(b) - this is incorrect; the rule is log(a x b) = log(a) + log(b)

• Using base 1 or negative base - base must be positive and not equal to 1