Bodhee Prep-Online CAT Coaching | Online CAT Preparation | CAT Online Courses

Get 10% OFF on CAT 25 Courses. Code: BODHEE10 Valid till 07th April Enroll Now

CAT 2018 [SLOT 2] Quant Question with Solution 34

Question:
\(\frac{1}{{{{\log }_2}100}} - \frac{1}{{{{\log }_4}100}} + \frac{1}{{{{\log }_5}100}} - \frac{1}{{{{\log }_{10}}100}} + \frac{1}{{{{\log }_{20}}100}} - \frac{1}{{{{\log }_{25}}100}} + \frac{1}{{{{\log }_{50}}100}} = ?\)

  1. 1/2
  2. 0
  3. 10
  4. −4
Show Answer
Correct Answer: 1
We know that $\frac{1}{{{\log }_{b}}a}={{\log }_{a}}b$, therefore,
$\frac{1}{\log _{2} 100}-\frac{1}{\log _{4} 100}+\frac{1}{\log _{5} 100}-\frac{1}{\log _{10} 100}+\frac{1}{\log _{20} 100}-\frac{1}{\log _{25} 100}+\frac{1}{\log _{50} 100}$
= $\log _{100} 2-\log _{100} 4+\log _{100} 5-\log _{100} 10+\log _{100} 20-\log _{100} 25+\log _{100} 50$
=${{\log }_{100}}\left( \frac{2}{4}\times \frac{5}{10}\times \frac{20}{25}\times 50 \right)$
=${{\log }_{100}}10$
Using the relation ${{\log }_{{{a}^{m}}}}b=\frac{1}{m}{{\log }_{a}}b$
${{\log }_{100}}10={{\log }_{{{10}^{2}}}}10=\frac{1}{2}{{\log }_{10}}10=\frac{1}{2}$

CAT Online Course
Also Check: 841+ CAT Quant Questions with Solutions

CAT 2018 Slot-1


CAT 2018 Slot-2


CAT Quant Questions with Video Solutions

30 must do CAT Quant Questions with Video Solutions
CAT online Courses

FREE CAT Prep Whatsapp Group

CAT 2025 best online courses

Online CAT Courses