What is the difference between log and ln?

ln uses the mathematical constant e as its base. Common log uses base 10. A custom logarithm can use any positive base except 1.

Why can the logarithm value not be zero or negative?

No real exponent of a positive base produces zero or a negative number, so real logarithms are defined only for positive values.

Why can the base not equal 1?

Every power of 1 equals 1, so base 1 cannot uniquely represent other positive values and does not define a logarithm.

How are logarithms related to exponents?

They are inverse operations. If b raised to y equals x, then log base b of x equals y.

Math Calculators

Log Calculator

Calculate logarithms with any valid base and compare ln and log10 results.

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Value (x)Base (b)

log base 10 of 1000

Natural log, ln(x)

6.90775527898

Common log, log10(x)

About the Log Calculator

A logarithm answers the question: what exponent must the base be raised to in order to produce a value? For example, log base 10 of 1000 equals 3 because 10³ equals 1000.

Enter any positive value and a valid positive base other than 1. Quick presets switch between base 2, base 10 and the natural base e.

The calculator also displays ln and log10 side by side, which is useful when working across algebra, computing, science, finance and exponential growth problems.

Key features

Any positive base except 1
Base 2, base 10 and base e presets
Natural logarithm ln result
Common logarithm log10 result

How to use

1Enter the positive value whose logarithm you need.
2Enter a base or choose a quick base preset.
3Read the custom-base result and the ln and log10 comparisons.

Examples

Base-10 logarithm

Input: log base 10 of 1000

Output: 3

10 raised to the power 3 equals 1000.

Frequently asked questions

What is the difference between log and ln?: ln uses the mathematical constant e as its base. Common log uses base 10. A custom logarithm can use any positive base except 1.
Why can the logarithm value not be zero or negative?: No real exponent of a positive base produces zero or a negative number, so real logarithms are defined only for positive values.
Why can the base not equal 1?: Every power of 1 equals 1, so base 1 cannot uniquely represent other positive values and does not define a logarithm.
How are logarithms related to exponents?: They are inverse operations. If b raised to y equals x, then log base b of x equals y.

Open a related tool to prepare your files or refine the finished result.