Quick start
- Enter the value you want inside the logarithm.
- Enter the base, such as 2, 10, or e.
- Press Calculate log.
- Review the answer, ln(value), log10(value), power check, and steps.
- Use examples, recent answers, or Copy answer while comparing log problems.
What a logarithm means
A logarithm answers an exponent question. If log base b of x equals y, then b^y equals x. For example, log_2(8) equals 3 because 2^3 equals 8.
This is why the calculator shows a power check beside the main answer. It gives a quick way to confirm that the logarithm result matches the original value.
Valid inputs
The value inside a logarithm must be greater than zero. The base must also be greater than zero, and the base cannot equal 1.
Log answers can be positive, zero, or negative. For a base greater than 1, values above 1 create positive answers, value 1 creates answer 0, and values between 0 and 1 create negative answers.
Change of base
The calculator uses log_b(x) = ln(x) / ln(b). This lets it calculate logarithms for any valid base, even when the browser only gives direct natural-log and common-log math.
Common log and natural log
log10 means base 10. It is common in scientific notation, pH examples, decibels, and powers of 10.
ln means natural log, which uses base e. Natural logs show up often in growth, decay, calculus, and exponential models.
Examples from the log calculator
3
3
3
History, privacy, and copying
Recent log answers stay visible in the page while you work. The history is kept only in the current browser tab and is not sent to a server.
Copy answer copies the expression and result so you can paste it into notes, homework, a message, or another document.