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Omni-MATH / Suppose a real number x>1 satisfies log₂(log₄x)+log₄(log₁₆x)+log₁₆(log₂x)=0. Compute log₂(log₁₆x)+log₁₆(log₄x)+log₄(log₂x).

Problem

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problem

Suppose a real number x>1x>1 satisfies log2(log4x)+log4(log16x)+log16(log2x)=0\log _{2}\left(\log _{4} x\right)+\log _{4}\left(\log _{16} x\right)+\log _{16}\left(\log _{2} x\right)=0. Compute log2(log16x)+log16(log4x)+log4(log2x)\log _{2}\left(\log _{16} x\right)+\log _{16}\left(\log _{4} x\right)+\log _{4}\left(\log _{2} x\right).
Plain-text mathematical notation (without MathML)
Suppose a real number x>1 satisfies log₂(log₄x)+log₄(log₁₆x)+log₁₆(log₂x)=0. Compute log₂(log₁₆x)+log₁₆(log₄x)+log₄(log₂x).
Original LaTeX notation
Suppose a real number \(x>1\) satisfies \(\log _{2}\left(\log _{4} x\right)+\log _{4}\left(\log _{16} x\right)+\log _{16}\left(\log _{2} x\right)=0\). Compute \(\log _{2}\left(\log _{16} x\right)+\log _{16}\left(\log _{4} x\right)+\log _{4}\left(\log _{2} x\right)\).

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Source and history

task_id
09abab28-8686-5f7f-bc28-249ab97fc7d0
task_key
test--09abab28-8686-5f7f-bc28-249ab97fc7d0
task_revision_id
1
config / split
/ test

Official source

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