Exact
log₁₀(e)
Log of e
Answer
log(e) equals 0.434294481903. Note this is log base 10 of Euler's number — different from ln(e) which equals 1.
Decimal
0.434294481903
Formula
log(e) = 0.434294481903
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 e, so the result is the irrational number 0.434294481903.
2
Calculator method
Press log, type e, press =. Result: 0.434294481903. Most scientific calculators have a dedicated log key; the natural logarithm uses a separate ln key.
3
Cross-check
Verify by computing 10^0.434294481903. That returns approximately e. The two operations are inverses.
About this value
The common logarithm of e is 0.434294481903. Log of e ≈ 0.4343 is the reciprocal of the natural log of 10. It appears in change-of-base formulas: ln(x) = log(x) / log(e).
Frequently asked questions
What is log of e?
Log of e equals log₁₀(e) as an exact value, or 0.434294481903 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 e 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.