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 the value of x.

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

Best CAT Online Coaching
Try upto 40 hours for free
Learn from the best!

2IIM : Best Online CAT Coaching.

Best CAT Coaching in Chennai

CAT Coaching in Chennai - CAT 2022
Limited Seats Available - Register Now!

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 the value of x."

Hence, the answer is "34 or 31/4".

Choice C is the correct answer.

CAT Preparation Online | CAT Arithmetic Videos On YouTube

Other useful sources for Arithmetic Question | Logarithms and Exponents Sample Questions

CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT

Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now