Rewrite the log expression as a single log.
${\log }_{3}5+2{\log }_{3}x-{\log }_{3}2$

• A. ${\log }_3\frac{5-2x}{2}$
• B. ${\log }_{3}5x$
• C. ${\log }_3\frac{5x^2}{2}$
• D. ${\log }_3\frac{5+2x}{2}$

Answer: (C)

Verified step by step guidance

1. Identify the given expression: \(\log_3 5 + 2 \log_3 x - \log_3 2\).
2. Use the logarithm power rule to rewrite \(2 \log_3 x\) as \(\log_3 x^2\).
3. Rewrite the expression as \(\log_3 5 + \log_3 x^2 - \log_3 2\).
4. Apply the logarithm product rule to combine \(\log_3 5 + \log_3 x^2\) into \(\log_3 (5 \cdot x^2)\).
5. Use the logarithm quotient rule to combine \(\log_3 (5 x^2) - \log_3 2\) into a single logarithm: \(\log_3 \left( \frac{5 x^2}{2} \right)\).