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Log Calculator

Quickly find your Logarithm result with our free Log Calculator. Simple, fast, and accurate.

Logarithm

Result

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What is a Log Calculator?

A log calculator computes logarithms in any base. It helps solve exponential equations by finding the exponent needed to produce a given number from a specified base.

How to calculate logarithms manually (the formula)

logb(x) = y means by = x. For example, log10(1000) = 3 because 103 = 1000. The change-of-base formula: logb(x) = log(x) / log(b).

Example calculation

log10(1000) = ? 10? = 1000. Since 103 = 1000, log10(1000) = 3. ln(1000) = loge(1000) ≈ 6.908.

Common mistakes

  • Taking log of zero or negative numbers — Logarithms are only defined for positive arguments.
  • Confusing log and ln — log is base 10; ln is base e (natural log). They give different results for the same input.
  • Forgetting the change-of-base formula — Most calculators only have log and ln buttons. Use logb(x) = ln(x) / ln(b) for other bases.

Frequently asked questions

What is a logarithm?

To what power must the base be raised to get x?

What is the difference between log and ln?

log is base 10; ln is base e.

How do I calculate log in any base?

Use logb(x) = log(x) / log(b).

What is the log of 0?

Undefined. Only positive numbers have logarithms.

What is the log of 1?

0 in any base.

What are logarithms used for?

Exponential relationships, pH, decibels, and more.