Logarithm Calculator
Enter any positive value and base to get the logarithm with the change-of-base steps shown. It also gives the natural log (ln) and base-10 log, and explains the rule that log-base-b of x is the power b must be raised to.
How to use
- Enter a positive value for x and a positive base (the base cannot be 1).
- The result updates live, showing the change-of-base steps: log-base-b of x = ln x / ln b.
- Also check ln (base e) and log10 (base 10), which are shown alongside the main result.
Tips
- Remember the domain: x must be positive and the base must be positive and not equal to 1, or the log does not exist.
- Change-of-base means you only ever need one log button: log-base-b of x = ln x / ln b.
- Base-10 logs are used for scales like decibels and pH; natural logs appear in growth and decay problems.
Note: Definition of log: logᵦ x = y means bʸ = x. The base-10 log is usually called log and the base-e log is called ln.
Frequently Asked Questions (FAQ)
What can this logarithm calculator compute?
The log of any base using the change-of-base formula with the steps shown, plus the natural log (ln) and the base-10 log.
What values can I enter?
The value must be positive and the base must be positive and not equal to 1.
What is the difference between log and ln?
Log usually means the base-10 logarithm; ln means the natural logarithm, which uses base e.
How does the change-of-base step work?
Log-base-b of x equals ln(x) divided by ln(b). The tool shows this step so you can see how the answer was found.