Log Calculator
Evaluate logarithms with any base, including ln and log₁₀.
log base 10 of 1,000
3
ln (natural)
6.907755
log₁₀
3
log₂
9.965784
The inverse of exponents
log_b(x) asks: to what power must b be raised to reach x? Since 10³ = 1000, log₁₀(1000) = 3. Any base converts to any other by division — log_b(x) = ln(x) ÷ ln(b) — which is exactly how this calculator computes custom bases.
Why logs are everywhere
Logs compress multiplicative scales into additive ones: decibels, earthquake magnitude, pH, and interest doubling times are all logarithms. In algorithms, log₂ counts how many halvings reach 1 — the heart of binary search's speed.
Frequently asked questions
- How does the Log Calculator work?
- Evaluate logarithms with any base, including ln and log₁₀.
- Is the Log Calculator free to use?
- Yes. The Log Calculator is completely free, runs entirely in your browser, and requires no account or sign-up. Your inputs never leave your device.
Related calculators
Percentage Calculator
Solve any percentage problem: percent of, percent change, and more.
Fraction Calculator
Add, subtract, multiply, and divide fractions with simplified results.
Scientific Calculator
A full scientific calculator with trig, logs, and exponents.
Random Number Generator
Generate random numbers in any range, with or without repeats.