Log of −1 (Base 10)
Logarithm Calculator
What is log(−1)?
Answer
log(−1)
does not exist
log here is the common log, base 10.
10 raised to any power is a positive number, so the negative number −1 cannot be reached.
We look for y with 10y = −1.
The curve y = log x passes through (1, 0) and (10, 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
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Common log of nearby numbers
FAQ
What is log(−1)?
log(−1) does not exist
Does log(−1) exist in complex numbers?
Yes, in complex numbers: the principal value for x < 0 is log x = (ln|x| + iπ) / ln 10, so log(−1) = iπ / ln 10 ≈ 1.3644i. Among real numbers it does not exist.
What is e?
e ≈ 2.71828 is the base of the natural logarithm: ln x is the logarithm of x to base e, so ln e = 1. It is an irrational number, like π.
See Also
- Log Base 7 of 7 (log₇ 7)
- Log Base 7 of 8 (log₇ 8)
- Log Base 7 of 343 (log₇ 343)
- Log Base 8 of 1 (log₈ 1)
- Log Base 8 of 2 (log₈ 2)
- Log Base 8 of 4 (log₈ 4)
- Log Base 8 of 5 (log₈ 5)
- Log Base 9 of 1/81 (log₉(1/81))
- Log Base 9 of 3 (log₉ 3)
- Log Base 9 of 27 (log₉ 27)
- Log of −2 (Base 10)
- Log of 0 (Base 10)
- Log of 0.01 (Base 10)
- Log of 0.05 (Base 10)
- Log of 0.1 (Base 10)
- Log of 0.3 (Base 10)
- Log of 0.8 (Base 10)
- Log of 0.9 (Base 10)
- Log of 1 (Base 10)
- Log of 1.6 (Base 10)
- Десятичный логарифм −1 (lg(−1))
- Logaritmo decimal de −1 (log(−1))
- Logaritmo decimal de −1 (log(−1))