Simplify: \(\log_{10}\) 6 - 3 log\(_{10}\) 3 + \(\frac{2}{3} \log_{10} 27\)
A
3 \(\log_{10}^2\)
B
\(\log_{10}^2\)
C
\(\log_{10}^3\)
D
2 \(\log_{10}^3\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
log\(_{10}\) 6 - log\(_{10}\)3\(^3\) + log\(_{10}\) (\(\sqrt[3]{27}\))\(^2\)
= log \(_{10}\) 6 - log \(_{10}\) 27 + log\(_{10}\) 9
= log\(_{10}\) \(\frac{6 \times 9}{27}\)
= log\(_{10}\)2
Source: Myschool Past Questions Archive (Record #57197)