A System with $\lg$ Exponents

Problem

Positive real numbers $x, y, z$ satisfy

x^{\lg x}\, y^{\lg y}\, z^{\lg z} = 5, \qquad x^{\lg(yz)}\, y^{\lg(zx)}\, z^{\lg(xy)} = 2,

where $\lg$ denotes the base- $10$ logarithm. Find $xyz$ .

Answer

Solution

Difficulty	6/10
Topics	Substitution, algebra, Logarithms

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