Suppose `x;y;zgt0` and are not equal to 1 and `log x+log y+log z=0`. Find the value of `x^(1/log y+1/log z)xx y^(1/log z+1/log x)xx z^(1/logx+1/logy)`
Suppose `x;y;zgt0` and are not equal to 1 and `log x+log y+log z=0`. Find the value of `x^(1/log y+1/log z)xx y^(1/log z+1/log x)xx z^(1/logx+1/logy)` (base 10)
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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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