What does the Logarithm Calculator do?

Calculate log₁₀, ln, log₂ and custom base logarithms. Includes antilog and log rules. All calculations are performed in your browser using official UK rates and thresholds.

How accurate are the results?

This calculator uses standard mathematical algorithms and provides results accurate to the precision shown. For very large numbers or high-precision requirements, results are rounded to a reasonable number of decimal places.

Can I use this for schoolwork?

Yes. This calculator is suitable for GCSE, A-level and university-level mathematics. It follows standard mathematical conventions used in UK education.

Logarithm Calculator

Calculate log₁₀, ln, log₂ and custom base logarithms. Includes antilog and log rules.

Last updated: April 2026 · Source: BBC Bitesize — Logarithms

Number

Custom Base

log₁₀(100)

ln(100)

4.6051702

log₂(100)

6.6438562

log_10(100)

Also: 10^100 = 1.0000e+100 (antilog)

log rules: log(a×b) = log(a)+log(b) · log(a/b) = log(a)-log(b) · log(aⁿ) = n×log(a)

Disclaimer

This calculator is provided for informational purposes only and should not be considered as financial or tax advice. All calculations are performed locally in your browser — no personal data is collected or sent to our servers. Rates and thresholds are sourced from HMRC and GOV.UK and are updated for the current tax year. Always verify results with HMRC or consult a qualified professional before making financial decisions.

How It Works

A logarithm answers the question: to what power must a given base be raised to produce a particular number? For example, log base 10 of 1000 = 3 because 10^3 = 1000. This calculator handles common logarithms (base 10), natural logarithms (base e, written as ln) and custom bases.

Logarithms are the inverse of exponents. They are used in science (pH scale, Richter scale, decibels), finance (compound interest) and computing (algorithmic complexity). The calculator shows the conversion between different bases using the change-of-base formula: log_b(x) = ln(x) / ln(b).

Example: Calculating log₁₀(500)

log₁₀(500) = 2.6990
This means 10^2.6990 ≈ 500
ln(500) = 6.2146 (natural log)
log₂(500) = 8.9658 (log base 2)

Source: BBC Bitesize — Logarithms

Frequently Asked Questions

What does the Logarithm Calculator do?: Calculate log₁₀, ln, log₂ and custom base logarithms. Includes antilog and log rules. All calculations are performed in your browser using official UK rates and thresholds.
How accurate are the results?: This calculator uses standard mathematical algorithms and provides results accurate to the precision shown. For very large numbers or high-precision requirements, results are rounded to a reasonable number of decimal places.
Can I use this for schoolwork?: Yes. This calculator is suitable for GCSE, A-level and university-level mathematics. It follows standard mathematical conventions used in UK education.