Log Calculator – Aplicativy.

Enter a number and a base to find the logarithm, with the natural log shown alongside.

Reading logarithms

A logarithm answers a single question: to what power must the base be raised to produce this number? Because ten to the third power is one thousand, the base ten logarithm of one thousand is three. Logs turn multiplication into addition, which is why they underpin slide rules, decibels, pH, and the Richter scale.

Two bases dominate practice. Base ten is the common logarithm, written log, and base e is the natural logarithm, written ln, which appears throughout growth and decay problems. This tool shows both so you can move between them easily.

The formula

log_base(x) = ln(x) / ln(base)

Worked example

The base 10 log of 1000 is 3, because 10 to the 3rd power is 1000.

How to read your result

The logarithm answers the question: to what power must the base be raised to produce this number? Base 10 is the common log; base e is the natural log written ln.

Frequently asked questions

What is the difference between log and ln?: log usually means base 10, while ln is the natural log with base e.
Why must the number be positive?: Logarithms are undefined for zero and negative numbers.
What base should I use?: Use the base your problem specifies; 10 and e are the most common.

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