Log Base 3 of 1/9
Logarithm Calculator
What is log₃(1/9)?
Answer
log3(1/9) =
−2
log3 is the log base 3.
log3(1/9) is the power you raise 3 to, to get 1/9: 3y = 1/9.
3⁻² = 1/3² = 1/9 ✓
Answer point (1/9, −2).
The curve y = log3 x passes through (1, 0) and (3, 1) and rises: for x > 1 the log is positive, for 0 < x < 1 negative.
| Base | Notation | Value |
|---|---|---|
| e | ln(1/9) | ≈ −2.1972 |
| 10 | log(1/9) | ≈ −0.9542 |
| 2 | log₂(1/9) | ≈ −3.1699 |
| 3 | log₃(1/9) | −2 |
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
FAQ
What is log₃(1/9)?
log₃(1/9) = −2
How to find log₃(1/9) without a calculator?
Write 1/9 as a power of 3: 1/9 = 3⁻². The exponent is the answer: log₃(1/9) = −2.
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 2 of 27 (log₂ 27)
- Log Base 2 of 32 (log₂ 32)
- Log Base 2 of 64 (log₂ 64)
- Log Base 2 of 100 (log₂ 100)
- Log Base 2 of 128 (log₂ 128)
- Log Base 2 of 256 (log₂ 256)
- Log Base 2 of 1000 (log₂ 1000)
- Log Base 2 of 1024 (log₂ 1024)
- Log Base 2 of 32768 (log₂ 32768)
- Log Base 3 of 1 (log₃ 1)
- Log Base 3 of 2 (log₃ 2)
- Log Base 3 of 3 (log₃ 3)
- Log Base 3 of 4 (log₃ 4)
- Log Base 3 of 5 (log₃ 5)
- Log Base 3 of 6 (log₃ 6)
- Log Base 3 of 7 (log₃ 7)
- Log Base 3 of 8 (log₃ 8)
- Log Base 3 of 9 (log₃ 9)
- Log Base 3 of 27 (log₃ 27)
- Log Base 3 of 81 (log₃ 81)
- Логарифм 1/9 по основанию 3 (log₃(1/9))
- Logaritmo en base 3 de 1/9 (log₃(1/9))
- Logaritmo de 1/9 na base 3 (log₃(1/9))