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The `x , y , z` are positive real numbers such that `(log)_(2x)z=3,(log)_(5y)z=6,a n d(log)_(x y)z=2/3,` then the value of `(1/(2z))` is ............

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The correct Answer is:
5
` z = 8x^(3), z = 5^(6)y^(6), z = x^(2//3) y^(2//3)`
` rArr x = (z^(1//3))/2, y = (z^(1//6))/5`
` rArr z = 1/(2^(2//3)) z^(2//9) * (z^(2//18))/(5^(2//3))`
` rArr z^(2//3) = 1/((10)^(2//3)) or z = 1/(10)`
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CENGAGE PUBLICATION-LOGARITHM AND ITS PROPERTIES-Numerical Value Type
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