Logarithmic Calculator
Calculate logarithms with any valid base, compare common and natural logs, apply the change-of-base formula, and see a clear step-by-step breakdown with an interactive graph.
The logarithm argument must be greater than zero.
Use base 10, base e, base 2, or any valid custom base.
See the logarithm, equivalent exponential form, and verification.
log₁₀(1000) = ln(1000) ÷ ln(10) = 3
The argument must satisfy x > 0. The base must satisfy b > 0 and b ≠ 1. A base between 0 and 1 creates a decreasing logarithmic function, while a base greater than 1 creates an increasing function.
Logarithms are used in exponential equations, compound growth, pH, sound intensity, earthquake magnitude, computer science, information theory, and scientific notation.
What is a logarithm?
A logarithm answers the question: to what power must the base be raised to produce the given number?
What is the difference between log and ln?
In most calculator contexts, log means base 10 and ln means base e, where e is approximately 2.71828.
Can the base be a decimal?
Yes. The base may be any positive number except 1, including values between 0 and 1.
Why can’t I calculate log of zero or a negative number?
Real logarithms are only defined for positive arguments. Zero and negative values require other mathematical frameworks.
Results are estimates generated locally in your browser using standard mathematical formulas. They are for informational and educational purposes only and are not a substitute for verification in coursework, examinations or professional contexts requiring certified accuracy. VisionVix accepts no liability for decisions based on this tool's output.
This calculator is intended for educational and general mathematical use. Results are numerical approximations and should be independently verified for critical scientific or engineering work.
