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: log_{3}x + log_{x}3 = \\frac{17}{4}\\). Find the value of x.

- 3
^{4} - 3
^{1/4} - 3
^{4}or 3^{1/4} - 3
^{1/3}

3

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log_{3}x + log_{x}3 = \\frac{17}{4}\\)

Let y = log_{3}x

We know that log_{x}3 = \\frac{1}{log_3{x}}\\)

Hence log_{x}3 = \\frac{1}{y}\\)

Thus the equation can be written as y + \\frac{1}{y}\\) = \\frac{17}{4}\\)

4y^{2} + 4 = 17y

4y^{2} + 4 - 17y = 0

Solving the above equation we get y = 4 or \\frac{1}{4}\\)

If y = 4

log_{3}x = 4

Then x = 3^{4}

If y = \\frac{1}{4}\\)

log_{3}x = \\frac{1}{4}\\)

Then x = 3^{1/4}

The question is **"Find the value of x."**

Choice C is the correct answer.

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