Logarithm Calculator

Calculate logarithms with any base including natural log (ln) and common log (log10).

Result

Fill in the fields above, then press Calculate.

A logarithm calculator computes logarithms, antilogarithms, natural logarithms, and change-of-base conversions for any positive number.

Select the calculation mode: logarithm, antilogarithm, natural log, or change of base. Enter the value and base as needed. The calculator will compute the result and show equivalent representations.

Examples

Common log

log₁₀(1000) = 3, because 10³ = 1000

Natural log

ln(e²) = 2, because e² ≈ 7.389

Change of base

log₂(8) = ln(8)/ln(2) = 2.079/0.693 = 3

Frequently Asked Questions

What is a logarithm?
A logarithm answers the question: to what power must the base be raised to get a given number? log_b(x) = y means b^y = x.
What is the natural logarithm?
The natural logarithm (ln) uses base e ≈ 2.71828. It appears naturally in calculus, compound interest, and exponential growth/decay.
Why can you not take the log of a negative number?
In real numbers, logarithms are only defined for positive values because no real power of a positive base produces a negative result.
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Quick Tips

  • •Double-check your inputs — small errors lead to incorrect results.
  • •Use the change-of-base formula to convert between logarithm bases.
  • •Remember that log base 10 of 1000 is 3, which is a quick sanity check.