CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

CAT Questions | Logarithms and Exponents | Logarithm - Inequalities

The question is from Log and Exponents. This question is about logarithm - inequalities. We need to find out the base value of the log. 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 1: If log2X + log4X = log0.25√6 and x > 0, then x is

  1. 6-1/6
  2. 61/6
  3. 3-1/3
  4. 61/3

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Explanatory Answer

Method of solving this CAT Question from Logs and Exponents: Logarithm with non-integer bases are slightly trickier. Have a go at this one!

log2x + log4x = log0.25√6
We can rewrite the equation as:
log2x + \\frac{log_2{x}}{log_2{4}}\\) = log0.25√6
log2x * \\frac{3}{2}\\) = log0.25√6
=> log2x * 3 = 2log0.25√6
=> log2x3 = -log46
=> log2x3 = \\frac{-log_2{6}}{log_2{4}}\\)
=> log2x3 = \\frac{-log_2{6}}{6}\\)

=> 2log2x3 = -log26
2log2x3 + log26 = 0
log26X6 = 0
6x6 = 1
x6 = \\frac{1}{6}\\)
x =

The question is "If log2X + log4X = log0.25 \\sqrt {6}\\) and x > 0, then x is"

Hence, the answer is "6-1/6".

Choice A is the correct answer.


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