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Logarithm Calculator

Calculate the logarithm of a number for any base.

Number must be greater than 0.
Natural (e)
Common (10)
Binary (2)
Custom
Base must be > 0 and not 1.
Log Base 10
2
log10(100) = 2
102 = 100
Comparison

Understanding Logarithms

Natural Logarithm (ln)

The natural logarithm is the logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.71828.

ln(x) = loge(x)

Commonly used in calculus and growth/decay models.

Common Logarithm (log)

The common logarithm is the logarithm with base 10. It is also known as the decimal logarithm.

log(x) = log10(x)

Often used in pH levels (acidity), sound intensity (decibels), and Richter scale.

Change of Base Formula

Most calculators only have buttons for ln and log10. To find a logarithm with a different base, use the Change of Base Formula:

logb(x) = ln(x) / ln(b)

This tool uses this method internally to calculate custom bases.

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