1.

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Answer»

Step-by-step EXPLANATION:

We have,

{(yz)}^{ log(y) - log(z) } \times {(zx)}^{ log(z) - log(x) } \times {(xy)}^{ log(x) - log(y) } \\

= {(yz)}^{ log( \frac{y}{z} ) } \times {(zx)}^{ log( \frac{z}{x} ) } \times {(xy)}^{ log( \frac{x}{y} ) } \\

= {(x)}^{ log( \frac{z}{x} ) + log( \frac{x}{y} ) } \times {y}^{ log( \frac{y}{z} ) + log( \frac{x}{y} ) } \times {z}^{ log( \frac{y}{z} ) + log( \frac{z}{x} ) }

= {(x)}^{ log(z) - log(y) } \times {(y)}^{ log(x) - log(z) } \times {(z)}^{ log(y) - log(x) }

= \frac{(x)^{ log(z) } }{ {(x)}^{ log(y) } } \times \frac{ {(y)}^{ log(x) } }{ {(y)}^{ log(z) } } \times \frac{ {(z)}^{ log(y) } }{ {(z)}^{ log(x) } }

= \frac{(x)^{ log(z) } }{ {(y)}^{ log(x) } } \times \frac{ {(y)}^{ log(x) } }{ {(z)}^{ log(y) } } \times \frac{ {(z)}^{ log(y) } }{ {(x)}^{ log(z) } }

= 1


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