Question

please answer me..... ​

Answer 1

Step-by-step explanation:

We have,

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

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

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

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

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

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

$= 1$