This is a question from the topic of **Logarithms,** which got rolled out in CAT 2018 Question Paper. This topic is heavily tested in the **CAT Exam**. For the past few years, there have been at least 2 questions from this topic in the CAT Question Paper. Every **CAT Exam** aspirant's **CAT Online Preparation ** is incomplete without mastering this topic. We suggest you to solve **CAT Previous Year Paper** to ace this topic. Try one right here!

Question 34 : \\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}) = ?

- 0
- \\frac{1}{2})
- -4
- 10

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We know that \\frac{1}{log_a b}) = log_{b} a

⟹ log_{100} 2 - log_{100} 4 + log_{100} 5 - log_{100} 10 + log_{100} 20 - log_{100} 25 + log_{100} 50

We also know that (- log_{a} b) = log_{a} (\\frac{1}{b}))

⟹ log_{100} (2 × \\frac{1}{4}) × 5 × \\frac{1}{10}) × 20 × \\frac{1}{25}) × 50)

⟹ log_{100} 10 = \\frac{1}{2})

The question is **"\\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}) = ?"**

Choice B is the correct answer

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