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Log Calculator

Calculate logarithms with any base — log, ln, log2, and log10.

Results

Log (custom base)2
Log₁₀2
Ln (natural log)4.605
Log₂6.644
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What is Log?

A logarithm is the inverse of exponentiation. log_b(x) = y means b^y = x. For example, log₁₀(100) = 2 because 10² = 100.

Logarithms are used in science (pH scale, Richter scale, decibels), finance (compound interest), and computer science (algorithm complexity).

Formula

log_b(x) = ln(x) / ln(b) log₁₀(x) = log(x) / log(10) ln(x) = natural logarithm (base e = 2.71828) log₂(x) = log(x) / log(2)

Rules: log(a×b) = log(a) + log(b) log(a/b) = log(a) − log(b) log(a^n) = n × log(a)

How to use this Log Calculator?

1. Enter the number. 2. Enter the base (default 10). 3. See log with your base, log₁₀, natural log, and log₂.

Frequently asked questions

What is ln?
ln is the natural logarithm — logarithm with base e (Euler's number, approximately 2.71828). It's widely used in calculus and continuous growth problems.
What is log₂ used for?
Log base 2 is fundamental in computer science. It tells you how many times you can halve a number. It determines binary search complexity, bit requirements, etc.
What is the log of 0?
Log(0) is undefined because no power of any positive base can equal 0.
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