Log Base 2 of −1
Logarithm Calculator
What is log₂(−1)?
Answer
log2(−1)
does not exist
log2 is the log base 2.
2 raised to any power is a positive number, so the negative number −1 cannot be reached.
We look for y with 2y = −1.
The curve y = log2 x passes through (1, 0) and (2, 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
Log base 2 of nearby numbers
FAQ
What is log₂(−1)?
log₂(−1) does not exist
Does log₂(−1) exist in complex numbers?
Yes, in complex numbers: the principal value for x < 0 is log₂ x = (ln|x| + iπ) / ln 2, so log₂(−1) = iπ / ln 2 ≈ 4.5324i. 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 Base 0.5 of 4
- Log Base 0.5 of 8
- Log Base 0.5 of 16
- Log Base 0.5 of 32
- Log Base 0.25 of 8
- Log Base 2 of 0 (log₂ 0)
- Log Base 2 of 0.5 (log₂ 0.5)
- Log Base 2 of 0.25 (log₂ 0.25)
- Log Base 2 of 0.125 (log₂ 0.125)
- Log Base 2 of 1 (log₂ 1)
- Log Base 2 of 1/3 (log₂(1/3))
- Log Base 2 of 1/6 (log₂(1/6))
- Log Base 2 of 2 (log₂ 2)
- Log Base 2 of 3 (log₂ 3)
- Log Base 2 of 4 (log₂ 4)
- Логарифм −1 по основанию 2 (log₂(−1))
- Logaritmo en base 2 de −1 (log₂(−1))
- Logaritmo de −1 na base 2 (log₂(−1))