Advanced Log Calculator – Antilog & Change of Base

A logarithm asks "which exponent produces this value". Since 2¹⁰ = 1024, log₂(1024) = 10. Calculators with only ln and log keys still reach any base through the change-of-base identity: log₄(8) = ln 8 / ln 4 = 2.079/1.386 = 1.5, meaning 4^1.5 = 8. The antilog reverses the operation — if log₁₀(x) = 3 then x = 10³ = 1000 — which is exactly how you recover a value from a log-scale chart. The tool also solves exponential equations: 3ˣ = 81 becomes x = log₃(81) = ln 81/ln 3 = 4. It prints the natural-log numerator and denominator for each computation, keeps 10+ significant digits, and links the three views (logarithmic, exponential, root) so you can sanity-check one against another: log₂(1024) = 10 ⇔ 2¹⁰ = 1024.

1. 1

   Choose the base

   e for ln, 10 for common log, or any custom base b

2. 2

   Enter the value

   The argument x must be positive

3. 3

   Apply change of base

   ln(x)/ln(b) is shown with both numerator and denominator

4. 4

   Use antilog to invert

   Raise the base to the result: bˣ recovers the original value

• 1

  log_b(x) exists only for x > 0 regardless of base

• 2

  Change of base: log₁₂(144) = ln 144/ln 12 = 2 — verify by 12² = 144

• 3

  Antilog in base 10 is just 10ˣ — the inverse typed on most calculators

• Taking the log of zero or a negative number, which is undefined

• Dividing in the wrong order: log_b(x) is ln(x)/ln(b), not ln(b)/ln(x)

• Confusing log₂(1024) = 10 with 1024 = 2×10

• Assuming log(x·y) = log x + log y fails — it holds; the error is applying it as log(x+y)