What's the difference between log and ln?

log typically refers to the common logarithm (base 10), while ln is the natural logarithm (base e ≈ 2.718). In some contexts, log might refer to natural logarithm, so it's important to check the convention being used.

Why can't I take the log of a negative number?

In real numbers, logarithms of negative numbers are undefined because no real power of a positive base can produce a negative result. However, complex logarithms can handle negative numbers.

What is the natural logarithm used for?

Natural logarithms are used in calculus, exponential growth/decay models, compound interest calculations, and many areas of physics and engineering where e appears naturally.

How do logarithms relate to exponents?

Logarithms and exponents are inverse operations. If y = bˣ, then x = log_b(y). This relationship makes logarithms useful for solving exponential equations.

Logarithm Calculator – Log, Ln, and Custom Base

Calculate logarithms with any base including common log (base 10), natural log (ln), and custom bases. Essential for exponential and logarithmic functions.

Logarithm Calculator – Log, Ln, and Custom Base

Calculate logarithms with any base including common log (base 10), natural log (ln), and custom bases. Essential for exponential and logarithmic functions.

Number*

Number to find the logarithm of (must be positive)

Base*

Logarithm base

Custom Base

Enter custom base (if selected above)

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Math visualization will appear here

Understanding Logarithms

A logarithm answers the question: "To what power must we raise the base to get this number?" For example, log₁₀(100) = 2 because 10² = 100.

Common Logarithm Types

Different logarithm bases:

Common log (log₁₀): Used in science, engineering, and pH calculations
Natural log (ln): Base e ≈ 2.718, used in calculus and exponential growth
Binary log (log₂): Used in computer science and information theory
Custom bases: Any positive number except 1 can be a logarithm base

How to Use This Calculator

Follow these simple steps to get accurate results:

Enter your number
Enter your base
Enter your custom base
Click the "Calculate" button to see your results
Review the detailed breakdown and explanation

Why Use Our Logarithm Calculator – Log, Ln, and Custom Base?

100% free and no registration required
Instant, accurate calculations with professional formulas
Mobile-friendly design that works on any device
Privacy-focused - your data never leaves your browser
Educational content to help you understand the results

Frequently Asked Questions

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