Exact
log₁₀(2)
Log of 2
Answer
log(2) equals 0.301029995664. This is the base-10 logarithm.
Decimal
0.301029995664
Formula
log(2) = 0.301029995664
Worked steps
1
Definition
log(x) (base 10) is the power you raise 10 to in order to get x. There is no clean integer power of 10 equal to 2, so the result is the irrational number 0.301029995664.
2
Calculator method
Press log, type 2, press =. Result: 0.301029995664. Most scientific calculators have a dedicated log key; the natural logarithm uses a separate ln key.
3
Cross-check
Verify by computing 10^0.301029995664. That returns approximately 2. The two operations are inverses.
About this value
The common logarithm of 2 is 0.301029995664. Log 2 ≈ 0.301 is one of the most-used non-trivial log values, appearing in audio (decibels), information theory, and decimal-to-binary digit conversions.
Frequently asked questions
What is log of 2?
Log of 2 equals log₁₀(2) as an exact value, or 0.301029995664 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 2 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.