Log Calculator

Calculate common logarithms, natural logarithms, custom-base logarithms, and inverse antilogs with this free log calculator.

Calculate Logarithms

log10(1000)
ln(2.718281828)
log3(81)
103
Your result will appear here.

How logarithms are calculated

Common log:
log10(x)

Natural log:
ln(x) = loge(x)

Custom base:
logb(x) = ln(x) ÷ ln(b)

Antilog:
bx

Why log calculations matter

Logarithms are used in algebra, science, finance, engineering, and computer science to solve exponential equations and work with growth and decay.

They make it easier to analyze powers, scales, and exponential relationships.

What your result means

Your result shows the logarithm or antilog value for the selected mode. Supporting values help explain the base used, exponent form, and decimal result.

This makes it easier to check algebra work, science equations, and exponential growth or decay calculations.

Log calculator tips

Frequently asked questions

What is a logarithm?

A logarithm tells you what exponent a base must be raised to in order to produce a number.

What is the difference between log and ln?

log usually means base 10, while ln means base e.

Can the number inside a log be negative?

No. In real-number logarithms, the input must be greater than 0.

What is an antilog?

An antilog is the inverse of a logarithm and converts back into exponential form.