How do you convert a value to a log scale?

To convert a value x to a log scale with base b, compute log_b(x) = ln(x) / ln(b). The result tells you how many times you need to multiply b by itself to get x.

Logarithmic Scale Converter

Understanding logarithmic scales

A logarithmic scale displays numerical data over a very wide range of values in a compact way. Instead of increasing in equal increments, each interval on a log scale is a multiple of the previous one. This is particularly useful for data that spans several orders of magnitude, such as in acoustics (decibels), earthquake intensity (Richter scale), or acidity (pH).

On a base-10 log scale, moving one unit to the right multiplies the value by 10. For example, log‍10(1) = 0, log‍10(10) = 1, and log‍10(100) = 2. This tool helps visualize where a given number falls on such a scale, making it easier to grasp the relative size of values that differ greatly.

How to use

Enter a positive value to convert to its logarithmic representation.
Choose a base: 10 (common log), 2 (binary log), e (natural log), or a custom base.
Click Calculate to see the log value and its position on the log scale.
The canvas visual shows tick marks at each power of the base, with your value highlighted.
Use Copy to save the result, or Reset to start over.