Log Calculator

Professional calculator tool for accurate calculations and analysis. Fast, reliable, and easy to use for personal and business needs.

Logarithm Calculator

Calculate logarithms, antilogs, and perform logarithmic operations with any base

Calculation Type

Number to find logarithm of

Base of logarithm (must be > 0 and ≠ 1)

📐 Common Logarithms

🧮 Logarithm Properties

log₍b₎(xy) = log₍b₎(x) + log₍b₎(y)
log₍b₎(x/y) = log₍b₎(x) - log₍b₎(y)
log₍b₎(x^n) = n·log₍b₎(x)
log₍b₎(b) = 1
log₍b₎(1) = 0

Main Result

log₍10₎(100)

2

Natural Log

4.60517

ln(x) = log₍ₑ₎(x)

Common Log

2

log₁₀(x)

Binary Log

6.643856

log₂(x)

Antilog (base 10)

1.000e+100

10^100

Base 2 Result

6.643856

log₍2₎(100)

Different Notations

Exponential:
2.0000e+0
Scientific:
2.00000
Engineering:
2.000 × 10^0

Function Properties

Domain: (0, ∞)
Range: (-∞, ∞)
Vertical asymptote: x = 0 (vertical)
Inverse function: y = 10^x

Step-by-Step Solution

1Calculate: log₍10₎(100)
2Using change of base formula: log₍10₎(100) = ln(100) / ln(10)
3ln(100) = 4.605170
4ln(10) = 2.302585
5Result: 4.605170 / 2.302585 = 2.000000
6Verification: 10^2.000000 ≈ 100.00

1Mastering Log Calculations

Calculate logarithms with various bases including natural and common logs. Whether you're a student, educator, or professional, understanding the mathematical principles behind log will enhance your problem-solving abilities. This guide breaks down complex concepts into understandable components and provides practical applications for real-world scenarios.

Mathematical Foundations

The underlying mathematics involves fundamental principles that have wide-ranging applications. Understanding these concepts helps you: • Verify calculator results manually • Apply knowledge to related problems • Develop mathematical intuition • Solve more complex variations • Teach others effectively

Step-by-Step Problem Solving

Approach problems systematically: 1. Identify what you're solving for 2. Gather all necessary information 3. Choose the appropriate formula 4. Perform calculations carefully 5. Verify results make sense 6. Consider alternative methods


2Real-World Applications

Mathematical concepts aren't just theoretical - they have practical applications in many fields.

Professional Applications

Professionals in various fields use these calculations: • Engineers for design and analysis • Scientists for research and experiments • Financial analysts for modeling • Architects for planning and construction • Data scientists for analysis and predictions

Educational Value

For students and educators: • Builds foundational math skills • Develops logical thinking • Prepares for advanced topics • Provides exam preparation • Enables peer tutoring and collaboration

This comprehensive guide is regularly updated to ensure accuracy. Last reviewed: 7/25/2025

Frequently Asked Questions

How accurate are the calculations?

Our calculators use industry-standard formulas and algorithms, regularly tested for accuracy. For critical decisions, verify with professionals.

Can I save my calculations?

You can bookmark pages with your inputs, take screenshots, or use your browser's print function to save results for future reference.

Is my data private?

All calculations happen in your browser. We don't store or transmit your input data, ensuring complete privacy.