Logarithm Calculator

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.

Base b

Argument x (>0)

log_10(100)

log₂(100)6.64385619

ln(100)4.605170186

log₁₀(100)2

log_10(100)2

Solution steps (change of base)

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

Common logarithms

x	log₂x	ln x	log₁₀x
2	1	0.693	0.301
3	1.585	1.099	0.477
5	2.322	1.609	0.699
10	3.322	2.303	1
100	6.644	4.605	2
1024	10	6.931	3.010

💡 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

Enter values or expressions: type directly into the Logarithm Calculator — keyboard friendly.
Instant results: everything computes live as you type, no button needed.
Follow the steps: the result panel shows full working and formula substitution.
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.

Related Guides

Source & Updates

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

Last updated: 2026-08-04

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

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.