Rewrite the difference as a single logarithm. Further simplify if possible.
${\log }_{5}24-{\log }_{5}8$

• A. ${\log }_{5}3$
• B. ${\log }_5\left(\frac{1}{3}\right)$
• C. ${\log }_{5}16$
• D. $-{\log }_{5}16$

Answer: (A)

Verified step by step guidance

1. Recall the logarithmic property for the difference of logs with the same base: \(\log_b A - \log_b B = \log_b \left( \frac{A}{B} \right)\).
2. Apply this property to the given expression \(\log_5 24 - \log_5 8\) to rewrite it as a single logarithm: \(\log_5 \left( \frac{24}{8} \right)\).
3. Simplify the fraction inside the logarithm: \(\frac{24}{8} = 3\).
4. Rewrite the expression using the simplified fraction: \(\log_5 3\).
5. Check if the logarithm can be simplified further; since 3 is already in simplest form, the expression \(\log_5 3\) is the final simplified form.