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NDA 2011
Exam
NDA
Year
2011
Subject
Mathematics
Chapter
Basics of Mathematics

NDA 2011 · Mathematics · Basics of Mathematics

What is the value of _ 10 ((9)/(8))- _ 10 ((27)/(32))+ _ 10...

What is the value of log⁡10\log _{10}\left(\frac{9}{8}\right)-\log _{10} (2732)+log⁡10(34)?\left(\frac{27}{32}\right)+\log _{10}\left(\frac{3}{4}\right)?

Options

  1. A3
  2. B2
  3. C1
  4. D0

Correct answer

D. 0

Step-by-step solution

log⁡109−log⁡108−log⁡1027+log⁡1032+log⁡103−log⁡104⇒2log⁡103−3log⁡102−3log⁡103+5log⁡102+log⁡103−21log⁡102⇒3log⁡103−3log⁡103+5log⁡102−5log⁡102⇒0\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}
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