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Logarithm Calculator

Math Calculators

log, ln and log with any base

Quick Answer

Logarithm Calculator: log, ln and log with any base. Logarithm Calculator uses standard math formulas to compute accurate results instantly.

log_10(100)

2

log₂(100)6.64385619
ln(100)4.605170186
log₁₀(100)2
log_10(100)2

Solution steps (change of base)

  1. 1log_b(x) = ln(x) / ln(b)
  2. 2ln(100) = 4.605170186；ln(10) = 2.302585093
  3. 3log_10(100) = 4.605170186 ÷ 2.302585093 = 2
  4. 4Check: 10^2 ≈ 100

Common logarithms

xlog₂xln xlog₁₀x
210.6930.301
31.5851.0990.477
52.3221.6090.699
103.3222.3031
1006.6444.6052
1024106.9313.010

💡 Logarithms compress huge scales: pH = −log₁₀[H⁺], decibels = 10·log₁₀(P/P₀), Richter magnitude is log₁₀-based — each +1 means 10× amplitude. Binary log (log₂) measures information in bits.

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How to Use

  1. Enter values or expressions: type directly into the Logarithm Calculator — keyboard friendly.
  2. Instant results: everything computes live as you type, no button needed.
  3. Follow the steps: the result panel shows full working and formula substitution.
  4. Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

  • Logarithm Calculator is a free online math tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: log, ln and log with any base.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Logarithm Calculator formula

Logarithm Calculator uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Logarithm Calculator?
Open the page and fill in the input fields — results update automatically. log, ln and log with any base.
Are the results accurate?
Yes. All calculations use standard mathematical formulas and are verified for accuracy.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required — just open and use.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. All calculations run locally in your browser. Nothing is uploaded or stored.

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Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Maintained and periodically reviewed by the YiJianSuan editorial team — review process in ourEditorial Policy.

Cite this page: YiJianSuan. Logarithm Calculator[EB/OL]. https://www.yijiansuan.com/en/c/math/logarithm

Results provided by this tool are for reference only and do not constitute professional advice.