Log Base 2 of 1/3

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Log base
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What is log₂(1/3)?

Answer

log2(1/3) ≈
−1.5850

log2 is the log base 2.

≈ — the logarithm is irrational; the value is rounded to 4 decimal places.

log2(1/3) is the power you raise 2 to, to get 1/3: 2y = 1/3.

2⁻² = 1/4 < 1/3 < 1/2 = 2⁻¹, so −2 < log2(1/3) < −1

log2(1/3) = ln(1/3) / ln 2 ≈ −1.098612 / 0.693147 ≈ −1.5850

Oxy1

Answer point ≈ (1/3, −1.5850).

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.

Log of 1/3 in different bases
BaseNotationValue
eln(1/3)≈ −1.0986
10log(1/3)≈ −0.4771
2log₂(1/3)≈ −1.5850

See Also

Recalculate with different values ↑

Log base 2 of nearby numbers

xlog₂ x
0.125−3
1/6≈ −2.5850
0.25−2
1/3≈ −1.5850
0.5−1
10
21

FAQ

What is log₂(1/3)?

log₂(1/3) ≈ −1.5850

How to calculate log₂(1/3) on a calculator?

Divide the natural logs: log₂(1/3) = ln(1/3) / ln 2 ≈ −1.098612 / 0.693147 ≈ −1.5850.

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