Exact
3
Log of 1000
Answer
log(1000) equals 3. This is the base-10 logarithm.
Decimal
3
Formula
log(1000) = 3
Worked steps
1
Definition
log(x) (base 10) is the power you raise 10 to in order to get x. Since 10^3 = 1000, log(1000) = 3.
2
Calculator method
Press log, type 1000, press =. Result: 3. Most scientific calculators have a dedicated log key; the natural logarithm uses a separate ln key.
3
Cross-check
Verify by computing 10^3. That returns 1000 exactly. The two operations are inverses.
About this value
The common logarithm of 1000 is 3. Logarithms of powers of ten are integers — log 10 = 1, log 100 = 2, log 1000 = 3, log 10,000 = 4.
Frequently asked questions
What is log of 1000?
Log of 1000 equals 3 as an exact value, or 3 as a decimal. The exact form is what you'd typically write in exam working; the decimal is what your calculator displays.
Is this log base 10 or natural log?
This is base-10 (common log). On most calculators the log key gives base 10 and the ln key gives natural log (base e). Log of 1000 as a natural log would be different — for example, ln(100) ≈ 4.6052, but log(100) = 2.
How do I calculate this manually?
For powers of 10, count the zeros: log 10 = 1, log 100 = 2, log 1000 = 3. For other values, no exact integer answer exists — use a calculator. The change-of-base formula log_b(x) = ln(x) / ln(b) lets you compute logs in any base from natural log.
Where does this value show up?
Common logs appear in pH calculations (chemistry), decibels (audio), and order-of-magnitude estimates. log 2 ≈ 0.301 is a constant used in computer science and information theory.