If log x = frac{log y}{2} = frac{log z}{5},th | vedclass

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(C) Let $\frac{\log x}{1} = \frac{\log y}{2} = \frac{\log z}{5} = k$.Then,$\log x = k$,$\log y = 2k$,and $\log z = 5k$.We need to find the value of $x

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(C) Let $\frac{\log x}{1} = \frac{\log y}{2} = \frac{\log z}{5} = k$.Then,$\log x = k$,$\log y = 2k$,and $\log z = 5k$.We need to find the value of $x^{4} \cdot y^{3} \cdot z^{-2}$.Taking the logarithm of the expression,we get:$\log(x^{4} \cdot y^{3} \cdot z^{-2}) = 4 \log x + 3 \log y - 2 \log z$.Substituting the values of $\log x, \log y,$ and $\log z$ in terms of $k$:$= 4(k) + 3(2k) - 2(5k)$$= 4k + 6k - 10k$$= 10k - 10k = 0$.Since $\log(x^{4} \cdot y^{3} \cdot z^{-2}) = 0$,it follows that $x^{4} \cdot y^{3} \cdot z^{-2} = 10^{0} = 1$.

If $\log x = \frac{\log y}{2} = \frac{\log z}{5}$,then $x^{4} \cdot y^{3} \cdot z^{-2} = $

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