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(D) Given that ${\log _{10}}x = y$. We need to find the value of ${\log _{1000}}{x^2}$. Using the property of logarithms ${\log _{{a^n}}}{b^m} = \frac

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$\frac{2y}{3}$

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(D) Given that ${\log _{10}}x = y$. We need to find the value of ${\log _{1000}}{x^2}$. Using the property of logarithms ${\log _{{a^n}}}{b^m} = \frac{m}{n}{\log _a}b$,we can write: ${\log _{1000}}{x^2} = {\log _{{10^3}}}{x^2} = \frac{2}{3}{\log _{10}}x$. Substituting the given value ${\log _{10}}x = y$,we get: $\frac{2}{3}y$.

If ${\log _{10}}x = y$,then the value of ${\log _{1000}}{x^2}$ is

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