The question is from Log and Exponents. We can solve this easily using log identities. We need to find out the value of a log given an 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 8: log_{x}y + log_{y}x^{2} = 3. Find log_{x}y^{3}.

- 4
- 3
- 3
^{1/2} - 3
^{1/16}

3

4,000 off on CAT '22 Online courses

Valid until 25th July

Online Batches Available Now!

log_{x}y + log_{y}x^{2} = 3

Let a = log_{x}y

log_{x}3 = \\frac{1}{log_3{x}}\\)

log_{y}x^{2} = 2log_{y}x

We know that log_{y}x = \\frac{1}{log_x{y}}\\)

Hence form above log_{y}x = \\frac{1}{a}\\)

Now rewritting the equation log_{x}y + log_{y}x^{2} = 3

Using a we get a + \\frac{2}{a}\\) = 3

i.e., a^{2} - 3a + 2 = 0

Solving we get a = 2 or 1

If a = 2, Then log_{x}y = 2 and log_{y}x^{3} = 3

log_{x}y = 3 * 2 = 6

Or

If a = 1, Then log_{x}y = 1 and log_{y}x^{3} = 3

log_{x}y = 3 * 1 = 3

The question is **"Find log _{x}y^{3}."**

Choice B is the correct answer.

CAT 2021

Enroll at

44,000/-

Online Classroom Batches Starting Now!

Copyrights © All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Phone:** (91) 44 4505 8484

**Mobile:** (91) 99626 48484

**WhatsApp:** WhatsApp Now

**Email: **prep@2iim.com