Evaluate \(\frac{2\log_{3} 9 \times \log_{3} 81^{-2}}{\log_{5} 625}\)
A
4
B
-32
C
-8
D
16
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\frac{2\log_{3} 9 \times \log_{3} 81^{-2}}{\log_{5} 625}\)
= \(\frac{2\log_3 3^2 \times \log_3 (3^4)^{-2}}{\log_5 (5^4)}\)
= \(\frac{4\log_3 3 \times -8\log_3 3}{4\log_5 5}\)
= -8.
Source: Myschool Past Questions Archive (Record #55393)