CalKit

Logarithm Calculator

Calculate logarithm with any base.

log10(100)
2

밑이 10인 로그

다양한 로그 값

log10(100)2
ln(100) [자연로그]4.605170186
log₂(100)6.6438561898
log₁₀(100)2

밑 변환 공식

공식log_b(x) = ln(x) / ln(b)
적용log10(100) = ln(100) / ln(10)
계산4.605170186 / 2.302585093 = 2

Overview

The Logarithm Calculator computes logarithms with any base. It supports common logarithms (log₁₀), natural logarithms (ln), and custom-base logarithms, useful for solving exponential equations and scientific computations.

Formula

Definition: log_b(x) = y ↔ b^y = x

Change of base: log_b(x) = log(x) / log(b) = ln(x) / ln(b)

Log rules:
log_b(MN) = log_b(M) + log_b(N)
log_b(M/N) = log_b(M) - log_b(N)
log_b(M^k) = k × log_b(M)
log_b(1) = 0, log_b(b) = 1

How to Use

  1. 1Select the base (10, e, 2, or custom).
  2. 2Enter the argument x (x > 0).
  3. 3The logarithm value is calculated automatically.

Tips

  • ✔Common log (log₁₀) is useful for counting digits: digits of n = floor(log₁₀(n)) + 1.
  • ✔Natural log (ln) is used most frequently in calculus and science.
  • ✔log₂ is essential in computer science for binary search and algorithm complexity analysis.

FAQ

Q. What is the difference between common log and natural log?

Common log (log or log₁₀) has base 10, while natural log (ln or logₑ) has base e (≈2.71828). Common log is used in engineering and everyday applications; natural log is preferred in mathematics and science.

Q. Can you take the log of a negative number?

In the real number system, the argument of a logarithm must be positive. Logarithms of negative numbers are only defined in the complex number domain and are not used in typical calculations.

Q. How are logarithms used in real life?

Earthquake magnitude (Richter scale), sound intensity (decibels), pH (acidity), information entropy, and population growth models all use logarithms. They convert very large ranges of data into manageable scales.

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