If \(\log_{10}y + 3\log_{10}x \geq \log_{10}x\), express y in terms of x.

A.

\(y \geq \frac{1}{x}\)

B.

\(y \leq \frac{1}{x}\)

C.

\(y \leq \frac{1}{x^{2}}\)

D.

\(y \geq \frac{1}{x^{2}}\)

Correct answer is D

\(\log_{10}y + 3\log_{10}x \geq \log_{10}x\)

\(\implies \log_{10}y \geq \log_{10}x - 3 \log_{10}x \)

\(\log_{10}y \geq -2\log_{10}x = \log_{10}y \geq \log_{10}x^{-2}\)

\(\log_{10}y \geq \log_{10}(\frac{1}{x^{2}}) \implies y \geq \frac{1}{x^{2}}\)