Logarithm Calculator

📋 How to use this calculator

1. Choose the "Compute Log" tab to compute log_b(x); enter the base b (e.g., 2, 10, or e) and a positive number x.
2. For antilog, use the "Antilog" tab with a base and logarithm value as input; result = b^y.
3. On the "Equation" tab, enter a log equation of the form log_b(ax+c) = d to solve for x.
4. Verify logarithm properties on the "Properties" tab by entering two numbers to see proofs of the addition, subtraction, and exponent rules.
5. Use the standard log reference table (log 2 ~ 0.301, log 3 ~ 0.477, ln 2 ~ 0.693) for manual validation.
6. Watch the domain: x must be > 0 and b > 0 with b != 1, otherwise the result is undefined.

🧮 Logarithm and Change of Base

• b = logarithm base (b > 0 and b != 1)
• x = numerus or argument (x > 0)
• y = logarithm value (real number)
• ln = natural logarithm with base e ~ 2.71828
• log = base-10 logarithm (common logarithm)

Key properties: log(ab) = log(a) + log(b), log(a/b) = log(a) - log(b), log(a^n) = n * log(a).

💡 Worked example: Computing log_2(50)

Result: log_2(50) ~ 5.6439, meaning 2 raised to the power 5.6439 gives 50.

❓ Frequently asked questions

📚 Sources & references

• OpenStax College Algebra - Logarithms — OpenStax (Rice University)
• Logarithm - NIST Digital Library of Mathematical Functions — National Institute of Standards and Technology
• IEEE Standard for Floating-Point Arithmetic (IEEE 754) — IEEE