Log Base 2 of 0
Logarithm Calculator
What is log₂ 0?
Answer
log2 0
does not exist
log2 is the log base 2.
2 raised to any power is greater than zero, so no power gives 0. The closer x gets to 0, the lower log2 x: log₂ 0.001 ≈ −9.9658.
We look for y with 2y = 0.
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 has no point at x = 0: the curve goes down along the y-axis.
| Base | Notation | Value |
|---|---|---|
| e | ln 0 | does not exist |
| 10 | log 0 | does not exist |
| 2 | log₂ 0 | 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 0?
log₂ 0 does not exist
What does log₂ x approach as x approaches 0?
It decreases without bound (to −∞): log₂ 0.001 ≈ −9.9658, log₂ 0.0001 ≈ −13.2877. There is no value at x = 0 itself.
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 −1 (log₂(−1))
- 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)
- Log Base 2 of 5 (log₂ 5)
- Логарифм 0 по основанию 2 (log₂ 0)
- Logaritmo en base 2 de 0 (log₂ 0)
- Logaritmo de 0 na base 2 (log₂ 0)