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MATH / For each real number x, let ⌊x⌋ denote the greatest integer that does not exceed x. For how many positive integers n is it true that n<1000 and that ⌊log₂n⌋ is a positive even inte…

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problem

For each real number xx, let ⌊x⌋\lfloor x \rfloor denote the greatest integer that does not exceed xx. For how many positive integers nn is it true that n<1000n<1000 and that ⌊log2n⌋\lfloor \log_{2} n \rfloor is a positive even integer?
Plain-text mathematical notation (without MathML)
For each real number x, let ⌊x⌋ denote the greatest integer that does not exceed x. For how many positive integers n is it true that n<1000 and that ⌊log₂n⌋ is a positive even integer?
Original LaTeX notation
For each real number $x$, let $\lfloor x \rfloor$ denote the greatest integer that does not exceed $x$. For how many positive integers $n$ is it true that $n<1000$ and that $\lfloor \log_{2} n \rfloor$ is a positive even integer?

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
2d6cf8de-51ee-5fdc-a73d-05751ce29592
task_key
intermediate~5falgebra--test--2d6cf8de-51ee-5fdc-a73d-05751ce29592
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import