Correct Answer: Option D

Explanation

\(\log_{5}(y^{2} x^{5} \div 125b^{\frac{1}{2}})\)

= \(\log_{5} y^{2} + \log_{5} x^{5} - [\log_{5} 125 + \log_{5} b^{\frac{1}{2}}\)

= \(2\log_{5} y + 5\log_{5} x - \log_{5} 5^{3} - \frac{1}{2} \log_{5} b\)

= \(2\log_{5} y + 5\log_{5} x - 3 - \frac{1}{2}\log_{5} b\)

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