Calculate the logarithm of any number in base 10, natural log (base e), base 2, or a custom base. Includes antilog and log rules reference.
Definition: logb(x) = y means by = x
Product Rule: logb(xy) = logb(x) + logb(y)
Quotient Rule: logb(x/y) = logb(x) − logb(y)
Power Rule: logb(xn) = n · logb(x)
Change of Base: logb(x) = ln(x) / ln(b) = log₁₀(x) / log₁₀(b)
Special Values: logb(1) = 0 | logb(b) = 1 | logb(bn) = n
A logarithm answers the question: "To what power must we raise the base to get this number?" For example, log₁₀(1000) = 3 because 10³ = 1000. Logarithms are the inverse of exponentiation. They are widely used in science, engineering, finance (compound growth), sound (decibels), earthquakes (Richter scale), and computer science (algorithm complexity).
The antilog (antilogarithm) is the inverse of a logarithm. For base 10, antilog(y) = 10y. For example, if log₁₀(x) = 2, then x = antilog(2) = 10² = 100. Antilogarithms are useful for converting logarithmic values back to their original scale, such as in pH chemistry or decibel calculations in acoustics.
This free log calculator helps you get accurate results instantly without needing to work through the math manually. Whether you need a quick estimate or a precise figure, having a reliable tool on hand saves time and reduces errors compared to manual calculation.
Small errors in math calculations can compound into significant problems. A 1% miscalculation in a budget or measurement can translate to hundreds or thousands of dollars in wasted resources, or result in having to redo work entirely. This calculator uses the standard formulas and methods to give you reliable results you can trust.
Is this calculator free? Yes — completely free with no account, login, or payment required. Use it as many times as you need.
How accurate are the results? This calculator uses the standard formulas for log calculations. Results are accurate for typical use cases. For specialized or high-stakes applications, consult a professional.
Does it work on mobile? Yes. This calculator is fully responsive and works on smartphones, tablets, and desktops.