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Suppose x , y ,z are not equal to 1 and ...

Suppose `x , y ,z` are not equal to 1 and `logx+logy+logz=0.` Find the value of `(x^(1/logy+1/logz))(y^(1/logz+1/logx))(z^(1/logx+1/logy))`

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Let `K = x^(1/log y+1/log z)xxy^(1/log z+1/log x)xxz^(1/log x+1/log y)`
` :. log K = log x[1/log y+1/log z]+log y [1/log z+1/log x]+log z [1/log x+1/log y]`
Putting ` log x + log y + log z = 0 `(given ), we get
` log x/log y + log z/log y =- 1, log y/log x + log z / log x =- 1, log x/log z + log y/log z =- 1`
`:.` R.H.S. of Eq. (i) =- 3
`rArr log_(10) K=- 3 or K = 10^(-3)`
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