A logarithm is the inverse of exponentiation. log_b(x) = y means b^y = x. For example, log₁₀(100) = 2 because 10² = 100.

What is the natural logarithm?

The natural logarithm (ln) uses base e ≈ 2.71828. It appears naturally in calculus, compound interest, population growth, and many physical processes.

What are common logarithm properties?

Key properties: log(ab) = log(a) + log(b); log(a/b) = log(a) - log(b); log(a^n) = n·log(a); log_b(1) = 0; log_b(b) = 1.

Why can't I take the log of a negative number?

Real logarithms are only defined for positive numbers. log(0) is undefined (approaches -∞), and log of a negative requires complex numbers.

A logarithm is the inverse of exponentiation. log_b(x) = y means b^y = x. For example, log₁₀(100) = 2 because 10² = 100.

What is the natural logarithm?

The natural logarithm (ln) uses base e ≈ 2.71828. It appears naturally in calculus, compound interest, population growth, and many physical processes.

What are common logarithm properties?

Key properties: log(ab) = log(a) + log(b); log(a/b) = log(a) - log(b); log(a^n) = n·log(a); log_b(1) = 0; log_b(b) = 1.

Why can't I take the log of a negative number?

Real logarithms are only defined for positive numbers. log(0) is undefined (approaches -∞), and log of a negative requires complex numbers.

Educational Tool — Estimates for educational purposes only. Not financial advice.Disclaimer

Logarithms are the inverse of exponentiation and appear throughout mathematics, science, and engineering. This calculator computes logarithms in any base, including the common log (base 10), natural log (base e), and binary log (base 2).

Logarithm Calculator

Calculate logarithms in any base including natural log (ln), common log (log₁₀), and binary log (log₂).

January 2026

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Logarithm

Common Log (log₁₀)

Natural Log (ln)

4.61

Binary Log (log₂)

6.64

Antilog (10^x)

10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

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Wally's Analysis uses GPT-4o-mini for educational interpretations. AI responses are not personalized financial advice and may be inaccurate. All core calculations are deterministic — AI only interprets results.AI Transparency →

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Industry-standard formulas vetted against IRS, SSA, BLS, CFPB. Client-side calculations. Regularly updated.

This calculator provides mathematical results for educational purposes. Always verify critical calculations independently.

Updated: January 2026 · Methodology

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