Logarithm Calculator

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

log₍10.00₎(100)

2.000000

All Bases

Common Log (log₁₀)2.000000
Natural Log (ln)4.605170
Binary Log (log₂)6.643856

Use the Logarithm Calculator above to calculate your results. Enter your values and see instant results — all calculations run in your browser.

Disclaimer: This calculator is for informational purposes only and does not constitute tax, financial, or legal advice. Results are estimates based on the information you provide and current rates. Always consult a qualified tax professional or financial advisor for advice specific to your situation.

How It Works

Our Logarithm Calculator simplifies the process of finding the logarithm of any number to any desired base. Whether you need natural logarithms (ln), common logarithms (log10), or binary logarithms (log2), this tool provides instant and accurate results, making complex calculations accessible for students, engineers, and scientists by 2026.

The calculator utilizes the change-of-base formula, log_b(x) = log_c(x) / log_c(b), where 'c' is typically a readily computable base like 'e' (for natural log) or '10' (for common log). For example, to calculate log base 5 of 125, it would compute ln(125) / ln(5) or log10(125) / log10(5).

Ensure your base is a positive number other than 1, and the number you're taking the logarithm of (the argument) is positive. A common mistake is attempting to calculate the logarithm of zero or a negative number, which is undefined in real numbers. Also, remember that ln is log base 'e' (approximately 2.71828).

Example: Calculating the binary logarithm of a 2026 data point

  1. 1 Input the number 4096 (representing a hypothetical 2026 data storage capacity in gigabytes) and select '2' as the base.
  2. 2 Click the 'Calculate' button. The calculator will perform log2(4096).
  3. 3 The result will be 12.
  4. 4 This means that 2 raised to the power of 12 equals 4096. In a computing context, this could represent the number of bits required to address 4096 unique memory locations.

Source: Khan Academy · Last updated: April 2026

Frequently Asked Questions

What is a logarithm in simple terms?
A logarithm answers the question: "What exponent do I need?" For example, log base 2 of 8 = 3 because 2³ = 8. It is the inverse of exponentiation.
What is the difference between ln and log?
ln (natural log) uses base e (2.71828...) and is common in science and calculus. log (common log) uses base 10 and is common in engineering. When written without a base, "log" usually means base 10 in the US.
How do you convert between log bases?
Use the change of base formula: log_b(x) = ln(x)/ln(b) = log(x)/log(b). For example, log base 3 of 81 = ln(81)/ln(3) = 4.394/1.099 = 4.

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