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Log Calculator
Find a common log (base 10), a natural log, or a logarithm with any base, and check it with the antilog.
The number you take the log of
Formula
y = log₁₀(x)
Enter an argument greater than 0.
This log calculator finds the common logarithm in base 10, the natural logarithm in base e, and a logarithm in any base you enter. The result updates as you type, and an antilog raises the base to that result so you can check that it returns the argument. A custom base is written with the change-of-base formula, the natural log of the argument divided by the natural log of the base, and values outside the domain are explained in words.
Log base 10, natural log, and any other base
Choose common log for base 10, natural log for base e, or a custom base, and enter an argument greater than 0. The result appears as you type, along with the antilog, which raises the base to that result so you can check it returns the argument. For a natural log, the inverse is e raised to the result.
A custom base uses the change-of-base formula, ln(x) divided by ln(base), with your numbers filled in. The argument must be greater than 0, and the base must be greater than 0 and not equal to 1, or the page explains that the logarithm is undefined.
Frequently Asked Questions
What is log base 10?
Log base 10 is the common logarithm. It is the exponent you put on 10 to get the argument. log10(1000) = 3 because 10 to the power 3 is 1000. log10(1) = 0 and log10(10) = 1. On a classroom calculator the log key usually means base 10, and the antilog is 10 raised to the result.
What is the natural log?
The natural log, written ln, is a logarithm with base e. The number e is about 2.71828. ln(1) = 0, and ln(e) = 1. The inverse of a natural log is e raised to the result.
What is the change of base formula?
The change-of-base formula rewrites a logarithm using natural logs: log base b of x equals ln(x) divided by ln(b). The same relationship works with common logs, as log10(x) divided by log10(b). log2(8) = ln(8) / ln(2) = 3.
Why is the log of a negative number undefined?
A real power of a positive base is always positive, so no real exponent makes the base equal a negative number. The log of a negative number is undefined in real numbers, and so is the log of 0. The argument has to be greater than 0. The base has to be greater than 0 and cannot be 1.