CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

CAT Questions | Logarithms and Exponents | Logarithm - Different bases

The question is from Log and Exponents. This questions is about Logarithm - Different bases. We need to find out the value of log in terms of a and b based on given another two log values. With every extra hour you log in for this topic, it becomes exponentially simpler. CAT Logarithms and Exponents is a favorite in CAT Exam, and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam

Question 6: log5x = a (This should be read as log X to the base 5 equals a) log20x = b. What is logx10?

  1. \\frac{a + b}{2ab}\\)
  2. (a + b) * 2ab
  3. \\frac{2ab}{a + b}\\)
  4. \\frac{a + b}{2}\\)

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Explanatory Answer

Method of solving this CAT Question from Logs and Exponents: When we change the base, Log questions become far tougher.

Given, log5x = a
log20x = b
logx5 = \\frac{1}{a}\\)
logx20 = \\frac{1}{b}\\)
logx\\frac{100}{5}\\) = \\frac{1}{b}\\)
logx100 - logn5 = \\frac{1}{b}\\)
=> 2logx10 - \\frac{1}{a}\\) = \\frac{1}{b}\\)
logx10 = \\frac{1}{2}\\)(\\frac{1}{a}\\) + \\frac{1}{b}\\))
logx10 = \\frac{a + b}{2ab}\\)

The question is "What is logx10?"

Hence, the answer is "\\frac{a + b}{2ab}\\)".

Choice A is the correct answer.


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