CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

CAT Questions | Logarithms and Exponents | Logarithm - Identities

The question is from Log and Exponents. We can solve this easily using log identities. We need to find out the value of x from the given equation. 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 7: log3x + logx3 = \\frac{17}{4}\\). Find x.

  1. 34
  2. 31/8
  3. 31/4
  4. 31/3

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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.

log3x + logx3 = \\frac{17}{4}\\)
Let y = log3x
We know that logx3 = \\frac{1}{log_3{x}}\\)
Hence logx3 = \\frac{1}{y}\\)
Thus the equation can be written as y + \\frac{1}{y}\\) = \\frac{17}{4}\\)
4y2 + 4 = 17y
4y2 + 4 - 17y = 0
Solving the above equation we get y = 4 or \\frac{1}{4}\\)
If y = 4
log3x = 4
Then x = 34
If y = \\frac{1}{4}\\)
log3x = \\frac{1}{4}\\)
Then x = 31/4

The question is "Find x."

Hence, the answer is "34".

Choice A is the correct answer.


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