Natural Log of −1
Logarithm Calculator
What is ln(−1)?
Answer
ln(−1)
does not exist
ln is the natural log, base e ≈ 2.71828.
e raised to any power is a positive number, so the negative number −1 cannot be reached.
We look for y with ey = −1.
The curve y = ln x passes through (1, 0) and (e, 1) and rises: for x > 1 the log is positive, for 0 < x < 1 negative.
The graph exists only to the right of the y-axis: there is no point at x = −1.
| Base | Notation | Value |
|---|---|---|
| e | ln(−1) | does not exist |
| 10 | log(−1) | does not exist |
| 2 | log₂(−1) | does not exist |
See Also
- Square Root Calculator - Calculate the square root of any number
- Simplify Square Root Calculator - Write any square root in simplest radical form, step by step
- Scientific Calculator with Memory & History - Free Engineering Calculator Online with Memory Function, Operation History, Logarithms & Trigonometry. Similar to ti-83, ti-84, ti-89
Natural log of nearby numbers
| x | ln x |
|---|---|
| −5 | does not exist |
| −2 | does not exist |
| −1 | does not exist |
| 0 | does not exist |
| 0.01 | ≈ −4.6052 |
| 0.1 | ≈ −2.3026 |
| 0.2 | ≈ −1.6094 |
FAQ
What is ln(−1)?
ln(−1) does not exist
Does ln(−1) exist in complex numbers?
Yes, in complex numbers: the principal value for x < 0 is ln x = ln|x| + iπ, so ln(−1) = iπ ≈ 3.1416i. Among real numbers it does not exist.
What does log without a base mean?
At school and on a calculator, log x without a base is the common log, base 10: log 100 = 2. In Python, math.log(x) is the natural log ln x; in Excel, LN is the natural log and LOG is base 10.
See Also
- Log of 200 (Base 10)
- Log of 512 (Base 10)
- Log of 1000 (Base 10)
- Log of 7000000 (Base 10)
- Log of e (Base 10)
- Log Base 13 of 13 (log₁₃ 13)
- Log Base 16 of 1 (log₁₆ 1)
- Log Base 25 of 5 (log₂₅ 5)
- Log Base 81 of 27 (log₈₁ 27)
- Log Base 100 of 10 (log₁₀₀ 10)
- Natural Log of −2 (ln(−2))
- Natural Log of −5 (ln(−5))
- Natural Log of 0 (ln 0)
- Natural Log of 0.01 (ln 0.01)
- Natural Log of 0.1 (ln 0.1)
- Natural Log of 0.2 (ln 0.2)
- Natural Log of 0.4 (ln 0.4)
- Natural Log of 0.5 (ln 0.5)
- Natural Log of 0.9 (ln 0.9)
- Natural Log of 1 (ln 1)
- Натуральный логарифм −1 (ln(−1))
- Logaritmo natural de −1 (ln(−1))
- Logaritmo natural de −1 (ln(−1))