Let $x, y, z>0$. Prove that $$\left(\lg\frac{y}{z}\right)^{-\lg x}+\left(\lg\frac{z}{x}\right)^{-\lg y} + \left(\lg\frac{x}{y}\right)^{-\lg z} \ge3$$
Someone can give me a hint? I really have no clue.
2026-03-25 09:29:49.1774430989
Let $x, y, z>0$. Prove that $\left(\lg\frac{y}{z}\right)^{-\lg x}+\left(\lg\frac{z}{x}\right)^{-\lg y}+\left(\lg\frac{x}{y}\right)^{-\lg z} \ge3$
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It's wrong. Try $\frac{y}{z}<1$ and $x=2$.