How does the Logarithm Calculator work?

log_b(x) = n means bⁿ = x Then: Common log (log₁₀): log(1000) = 3 because 10³ = 1000 Then: Natural log (ln): ln(e) = 1 because e¹ = e ≈ 2.718 Then: log_b(x) = log(x)/log(b) — change of base formula.

Can you give an example of how to use the Logarithm Calculator?

Example: Input log₁₀(100) gives a result of 2 (10² = 100).

Is the Logarithm Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Logarithm Calculator?

Our Logarithm Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

Toán học

Logarithm Calculator

Value

Base

A logarithm answers the question: "To what power must the base be raised to get this number?" log_b(x) = n means bⁿ = x. Logarithms compress enormous ranges and are used in sound (decibels), earthquakes (Richter scale), and pH.

Rule	Formula
Product	log(xy) = log(x) + log(y)
Quotient	log(x/y) = log(x) − log(y)
Power	log(xⁿ) = n·log(x)
Change of base	log_b(x) = ln(x)/ln(b)
Inverse	b^(log_b(x)) = x

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Did You Know?

A 9.0 earthquake releases about 31 times the energy of an 8.0, because the Richter scale is logarithmic (base 10). Each whole number represents 10× more ground motion.

References

›Logarithm — Wikipedia
›Logarithms — Khan Academy

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Logarithm Rules

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