Evaluate \(\frac{2\log_{3} 9 \times \log_{3} 81^{-2}}{\log_{5} 625}\)
Take Free Practice Test On 2026 JAMB UTME, Post UTME, WAEC SSCE, GCE, NECO SSCE
Correct Answer: Option C
Explanation:
\(\frac{2\log_{3} 9 \times \log_{3} 81^{-2}}{\log_{5} 625}\)
= \(\frac{2\log_3 3^2 \times \log_3 (3^4)^{-2}}{\log_5 (5^4)}\)
= \(\frac{4\log_3 3 \times -8\log_3 3}{4\log_5 5}\)
= -8.
\(\frac{2\log_{3} 9 \times \log_{3} 81^{-2}}{\log_{5} 625}\)
= \(\frac{2\log_3 3^2 \times \log_3 (3^4)^{-2}}{\log_5 (5^4)}\)
= \(\frac{4\log_3 3 \times -8\log_3 3}{4\log_5 5}\)
= -8.