Q161 / 270 · NDA 2011 (Phase 1) · Mathematics

What is the value of $\log _{10}\left(\frac{9}{8}\right)-\log _{10}\left(\frac{27}{32}\right)+\log _{10}\left(\frac{3}{4}\right)$ ?

  • A
    3
  • B
    2
  • C
    1
  • Correct answer
    D
    0

Solution

$\begin{gathered}\log _{10} 9-\log _{10} 8-\log _{10} 27+\log _{10} 32 \\ +\log _{10} 3-\log _{10} 4 \\ \Rightarrow 2 \log _{10} 3-3 \log _{10} 2-3 \log _{10} 3+5 \log _{10} 2 \\ +\log _{10} 3-21 \log _{10} 2 \\ \Rightarrow 3 \log _{10} 3-3 \log _{10} 3+5 \log _{10} 2-5 \log _{10} 2 \\ \Rightarrow 0\end{gathered}$

Hence, the correct answer is option: 'D'.

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