Evaluate \(\log_{10}(\frac{1}{3} + \frac{1}{4}) + 2\log_{10} 2 + \log_{10} (\frac{3}{7})\)
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Correct Answer: Option B
Explanation:
\(\log_{10} (\frac{1}{3} + \frac{1}{4}) + 2\log_{10} 2 + \log_{10} (\frac{3}{7})\)
\(\frac{1}{3} + \frac{1}{4} = \frac{7}{12}\)
= \(\log_{10} (\frac{7}{12} \times 2^{2} \times \frac{3}{7})\)
= \(\log_{10} 1 = 0\)
\(\log_{10} (\frac{1}{3} + \frac{1}{4}) + 2\log_{10} 2 + \log_{10} (\frac{3}{7})\)
\(\frac{1}{3} + \frac{1}{4} = \frac{7}{12}\)
= \(\log_{10} (\frac{7}{12} \times 2^{2} \times \frac{3}{7})\)
= \(\log_{10} 1 = 0\)