Logarithm Calculator
Calculate logarithms in any base, plus the natural log and log base 10.
Last updated · View algorithm, constants and default inputs (JSON)
About this calculator
A logarithm answers the question “what power do I raise this base to, to get that number?”. Log scales compress enormous ranges into readable ones, which is why they appear in sound, earthquakes and finance.
Worked example
calculated with the default values below
Number 1,000 · Base 10 Logarithm 3.000000 · Natural logarithm 6.907755 · Log base 10 3.000000 · Log base 2 9.965784
General background references
Disclaimer
These calculators give general mathematical results. They suit study, planning and estimation — verify anything that feeds a graded submission, a published figure or a financial commitment.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
log_b(x) = ln(x) ÷ ln(b); log10(x) = ln(x) ÷ ln(10); log2(x) = ln(x) ÷ ln(2)
- x
- argument (value)
- b
- logarithm base
- log
- base-b logarithm
- ln
- natural logarithm
Requires value > 0, base > 0 and base ≠ 1; logarithm output is the exponent whose power reproduces value.
Frequently asked questions
What does the inverse output show?
The inverse output simply repeats the entered value because base raised to log-base(value) equals the original value. It has been removed as a duplicate; the calculator still returns log base b, natural log, log base 10 and log base 2.