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Logarithm Calculator

log_b(x) with any base, including ln. Step-by-step working.

log₁₀(1000) = ?
Examples
Result
log₁₀(1000) = 3
Step-by-step explanation
  • A logarithm answers the question: what power must you raise the base to, to get the value?
  • logb(x) = y means by = x.
  • In our case: log10(1000) = 3 because 103 = 1000.
  • The calculator uses the change-of-base formula: logb(x) = ln(x) / ln(b).
Power ↔ logarithm
Power10^3 = 1000Logarithmlog_10(1000) = 3
Check
103 ≈ 1000
The result does indeed bring us back to the value x (up to rounding error).

How to use it

  • What is a logarithm? logb(x) is the power you must raise the base b to, to get x.
  • log₁₀ — base-10 (common) logarithm. Useful for logarithmic scales, pH, decibels.
  • ln — natural logarithm (base e ≈ 2.71828). Appears in exponential growth calculations.
  • log₂ — binary logarithm (base 2). Useful in computer science.
  • General — choose any positive base other than 1.
  • Required: x > 0. The base must be positive and not equal to 1.

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✍️ Written by the MathsUK teamChecked against the National Curriculum and GCSE specifications