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Logarithm Calculator

Logarithm Calculator is part of Toolspire and is ready as soon as this page loads. The change-of-base formula is ln(value) ÷ ln(base). A base of 1 and a value of 0 or less are rejected because those logarithms are not real numbers.

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On this page

What you can do here

Any base

10 and 2 are the checks. e, as 2.718281828, is allowed because the base is just a number.

Change of base, named

The detail shows the natural logs being divided, so a wrong base is visible.

Integers stay tidy

A result within a hair of a whole number is printed as that whole number.

The sequence

How to use the Logarithm Calculator

  1. 1

    Type the number first and the base second

    log10 of 1,000 is value 1000, base 10. Swapping them asks a different question.

  2. 2

    Try the two checks

    1,000 in base 10 is 3. 8 in base 2 is 3.

  3. 3

    Do not type a negative value

    The page will refuse it rather than invent an answer.

Worth knowing

  • Logarithm Calculator on Toolspire: log_b(a) = ln(a) ÷ ln(b).
  • log10(1000) = 3. log2(8) = 3.
  • The value must be positive. The base must be positive and not 1.
  • This is a real logarithm. It does not return a complex value for a negative number.

Same log, two natural logs

A calculator that only has a natural log can still do any base, because log_b(a) is ln(a) divided by ln(b). That is the whole page. Base 10 of 1,000 is ln(1000)/ln(10) = 3. Base 2 of 8 is ln(8)/ln(2) = 3. Base 1 would divide by ln(1), which is 0.

FAQ

Questions about Logarithm Calculator

Where does Logarithm Calculator run?

Logarithm Calculator runs in this tab on Toolspire. What you type or drop in is not sent to us and is not stored on a server.

What is log base 10 of 1,000?

3.

What is log base 2 of 8?

3. Two to the third is 8.

Why is base 1 rejected?

ln(1) is 0, so the change-of-base division is undefined. No power of 1 equals 1,000.

Can the number be negative?

Not on this page. Real logarithms are defined for positive numbers.

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