📊 Logarithm Calculator

Calculate log₂, log₁₀, natural log (ln), and custom base logarithms

Logarithm Reference

Common Logarithms

log₁₀(1)= 0
log₁₀(10)= 1
log₁₀(100)= 2
log₂(2)= 1
log₂(8)= 3
ln(e)= 1
ln(1)= 0

Logarithm Laws

log(xy) = log(x) + log(y)
log(x/y) = log(x) - log(y)
log(xⁿ) = n·log(x)
logₐ(x) = ln(x)/ln(a)Change of base formula

Related Tools

📊

Percentage Calculator

Calculate percentages

💰

Compound Interest

Exponential growth calculations

About Logarithm Calculator - Log2, Log10, Natural Log (ln)

Calculate logarithms with any base: log₂, log₁₀, natural log (ln), and custom bases. Step-by-step solutions included.

Our **Logarithm Calculator** computes logarithms with any base you need. Calculate common logarithm (log₁₀), natural logarithm (ln), binary logarithm (log₂), or logarithms with custom bases. Each result includes step-by-step explanations. For exponential growth analysis, see our Compound Interest Calculator.

Logarithms are the inverse of exponential functions—if b^x = y, then log_b(y) = x. They're fundamental in science, engineering, finance, and computer science. Log₂ is essential for computer science, log₁₀ for scientific notation, and ln for calculus. Explore more math tools like our Imaginary Number Calculator.

Understanding logarithmic scales helps interpret earthquake magnitudes (Richter scale), sound levels (decibels), and pH values. Our calculator handles change of base, logarithmic properties, and provides exact values when possible. For derivative applications, try our Tangent Line Calculator.

Key Features

Common log (log₁₀)
Natural log (ln)
Binary log (log₂)
Custom base support
Change of base formula
Antilog calculation
Step-by-step solutions

Why Use This Tool?

Multiple logarithm types
Educational explanations
High precision results
Understand the math
Science applications
Programming help

Common Use Cases

Computer Science: Calculate bit requirements and algorithm complexity.

Chemistry: Work with pH and pOH calculations.

Finance: Analyze compound growth and half-life.

Physics: Convert between logarithmic scales.

Related Tools

Imaginary Number Calculator

Complex number operations.

Compound Interest Calculator

Exponential growth.

Percentage Calculator

Percentage calculations.

How to Use

1

Enter the number to find the logarithm of

2

Select logarithm type (log₁₀, ln, log₂, or custom)

3

For custom base, enter the base value

4

Click Calculate

5

View result with explanation

Frequently Asked Questions

Comments & Feedback

Share your experience with this tool

Please solve the math problem to verify you're human