If log\(_{10}\)2 = 0.3010 and log\(_{10}\)3 = 0.4771, simplify: (Log\(_{10}\)8-log\(_{10}\)2) \div (Log\(_{10}\)9 - log\(_{10}\)2)
A
4
B
3
C
-0.92
D
-4
E
0.92
Verified Correct Answer: E.
Step-by-Step Mathematical Solution
\(\frac{\log 8 - \log 2}{\log 9 - \log 2} = \frac{2\log 2}{2\log 3 - \log 2}\)
Numerator: \(2 \times 0.3010 = 0.6020\)
Denominator: \(2 \times 0.4771 - 0.3010 = 0.6532\)
\(\frac{0.6020}{0.6532} = \mathbf{0.92}\)
Source: Myschool Past Questions Archive (Record #42319)