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 log_{2}X + log_{4}X = log_{0.25}√6 and x > 0, then x is

- 6
^{-1/6} - 6
^{1/6} - 3
^{-1/3} - 6
^{1/3}

6

Try upto 40 hours for free

Learn from the best!

Limited Seats Available - Register Now!

log_{2}x + log_{4}x = log_{0.25}√6

We can rewrite the equation as:

log_{2}x + \\frac{log_2{x}}{log_2{4}}\\) = log_{0.25}√6

log_{2}x * \\frac{3}{2}\\) = log_{0.25}√6

=> log_{2}x * 3 = 2log_{0.25}√6

=> log_{2}x^{3} = -log_{4}6

=> log_{2}x^{3} = \\frac{-log_2{6}}{log_2{4}}\\)

=> log_{2}x^{3} = \\frac{-log_2{6}}{6}\\)

=> 2log_{2}x^{3} = -log_{2}6

2log_{2}x^{3} + log_{2}6 = 0

log_{2}6X^{6} = 0

6x^{6} = 1

x^{6} = \\frac{1}{6}\\)

x =

The question is **"If log _{2}X + log_{4}X = log_{0.25} \\sqrt {6}\\) and x > 0, then x is"**

Choice A is the correct answer.

CAT 2024

Classroom Batches Starting Now! @Gopalapuram and @Anna nagar

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