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Omni-MATH / Suppose x,y, and z are real numbers greater than 1 such that begin{aligned} x^{log _{y} z} & =2, y^{log _{z} x} & =4, text { and } z^{log _{x} y} & =8 end{aligned} Compute …

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problem

Suppose x,yx, y, and zz are real numbers greater than 1 such that $$\begin{aligned} x^{\log _{y} z} & =2, \\ y^{\log _{z} x} & =4, \text { and } \\ z^{\log _{x} y} & =8 \end{aligned}$$ Compute logxy\log _{x} y.
Plain-text mathematical notation (without MathML)
Suppose x,y, and z are real numbers greater than 1 such that $$\begin{aligned} x^{\log _{y} z} & =2, \\ y^{\log _{z} x} & =4, \text { and } \\ z^{\log _{x} y} & =8 \end{aligned}$$ Compute log_(x)y.
Original LaTeX notation
Suppose $x, y$, and $z$ are real numbers greater than 1 such that $$\begin{aligned} x^{\log _{y} z} & =2, \\ y^{\log _{z} x} & =4, \text { and } \\ z^{\log _{x} y} & =8 \end{aligned}$$ Compute $\log _{x} y$.

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Source and history

task_id
f728759c-1de4-5048-9981-20362021e9e4
task_key
test--f728759c-1de4-5048-9981-20362021e9e4
task_revision_id
1
config / split
/ test

Official source

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