Математика

Logarithm Calculator

Value (x)

Base

🌐

Detailed Guide Coming Soon

We're working on a comprehensive educational guide for the Logarithm Calculator in your language. The content below is shown in English.

What is Logarithm Calculator?

▾

A logarithm calculator computes log base 10, natural log (ln), log base 2, and any other base. Logarithms are the inverse of exponentiation.

PrimeCalcPro provides professional-grade tools trusted by businesses and academics.

Формула

▾

f(x)log_b(x) = y means b^y = x; Change of base: log_b(x) = log_10(x) / log_10(b)

Variable Legend

▾

Symbol	Ime	Единица	Опис
x	Number	—	—
b	Base	—	Usually 10, e, or 2
y	Logarithm result	—	—

How to Logarithm Calculator

▾

1logₐ(x) = y means aʸ = x
2log₁₀(x): common logarithm
3ln(x): natural log, base e ≈ 2.71828
4Change of base: logₐ(x) = ln(x)/ln(a)

Worked Examples

▾

Example 1

Given:log₁₀(1000)

Резултат:3 (because 10³ = 1000)

Example 2

Given:ln(e²)

Резултат:2

Real-World Applications

▾

🏗️

Scientific and engineering calculations

🔬

Earthquake magnitude (Richter scale)

📊

Sound intensity (decibels)

🏥

pH calculations in chemistry

Logarithm Properties

▾

Property	Formula
Product rule	log(ab) = log(a) + log(b)
Quotient rule	log(a/b) = log(a) − log(b)
Power rule	log(aⁿ) = n×log(a)
Change of base	logₐ(x) = log(x)/log(a)
log(1)	Always = 0, any base

Frequently Asked Questions

▾

What's the difference between log, ln, and log₁₀?

log (no base) = log₁₀. ln = natural log (base e ≈ 2.718). log₂ = binary logarithm.

When do I use logarithms?

Solving exponential equations, measuring scales (pH, Richter, decibels), growth/decay rates.

Why is log₁₀ of 1000 equal to 3?

10³ = 1000, so log₁₀(1000) = 3. Logarithm is the inverse of exponentiation.

References

›Logarithms — Khan Academy

Споредете со

⇄

Logarithms vs Exponents

Mathematically verified

Reviewed October 2026

Our methodology

Добијте неделни математички совети

Придружете се на 12.000+ претплатници кои добиваат совети за калкулатори секоја недела.

🔒

100% Бесплатно

Никогаш без регистрација

✓

Точно

Проверени формули

⚡

Тековно

Резултати додека пишувате

📱

Мобилно

Сите уреди

Logarithm Calculator