Log Base 2 of 1000 (log₂ 1000)

What is log₂ 1,000?

Answer

log₂ 1,000 ≈

9.9658

log₂ is the log base 2.

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

log₂ 1,000 is the power you raise 2 to, to get 1,000: 2^y = 1,000.

2⁹ = 512 < 1,000 < 1,024 = 2¹⁰, so 9 < log₂ 1,000 < 10

log₂ 1,000 = ln 1,000 / ln 2 ≈ 6.907755 / 0.693147 ≈ 9.9658

Answer point ≈ (1,000, 9.9658), beyond the drawing (the arrow points to it).

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.

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