Logarithm Calculator

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

By Konstantin Iakovlev · Updated April 2026 · Source: Khan Academy

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

Taking the logarithm of a number to any base you choose reduces to a single entry here. Natural logarithms (ln), common logarithms (log10), and binary logarithms (log2) all return instant, accurate values, which keeps work that would otherwise stall students, engineers, and scientists moving as we head through 2026.

Behind the scenes the change-of-base formula does the work: log_b(x) = log_c(x) / log_c(b), where 'c' is some base that's easy to compute, usually 'e' for natural log or '10' for common log. To find log base 5 of 125, for instance, the tool evaluates ln(125) / ln(5), or equivalently log10(125) / log10(5).

Two conditions keep the result real: the base has to be positive and not equal to 1, and the argument—the number you're taking the log of—has to be positive. Asking for the logarithm of zero or a negative number is the usual stumbling block, because it has no value in the real numbers. It also helps to recall that ln is simply log base 'e', with '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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