This question is from Logarithms. Logarithms is one of the most commonly tested topics in the CAT exam. Questions from Exponents and Logarithms have appeared consistently in the CAT exam for the last several years. Questions that appear in CAT tests your basic understanding, like this question, which tests your understanding of the property of logarithms. This topic is easy to master if you practice lots of questions from the CAT Previous Year Question Paper. With every extra hour you log in for this topic, it becomes exponentially simpler.
Question 10 : \\frac{2ร4ร8ร16}{(log_{2}4)^{2}(log_{4}8)^{3}(log_{8}16)^{4}}) equals
To start with, we have, \\frac{2ร4ร8ร16}{(log_{2}4)^{2}(log_{4}8)^{3}(log_{8}16)^{4}})
Let's work on the denominator alone,
log24 = 2
log48 = \\frac{log8}{log4}) = \\frac{log_{2}8}{log_{2}4}) = \\frac{3}{2})
log816 = \\frac{log16}{log8}) = \\frac{log_{2}16}{log_{2}8}) = \\frac{4}{3})
So, the denominator becomes, 2 ร 2 ร \\frac{3}{2}) ร \\frac{3}{2}) ร \\frac{3}{2}) ร \\frac{4}{3}) ร \\frac{4}{3}) ร \\frac{4}{3}) ร \\frac{4}{3})
= 2 ร 4 ร 4 ร \\frac{4}{3})
And hence the fraction becomes, \\frac{2ร4ร8ร16}{2 ร 4 ร 4 ร 4/3})
= \\frac{2 ร 4 ร 8 ร 16 ร 3}{2 ร 4 ร 4 ร 4})
= 2 ร 4 ร 3 = 24
The question is "\\frac{2ร4ร8ร16}{(log_{2}4)^{2}(log_{4}8)^{3}(log_{8}16)^{4}}) equals"
Copyrights ยฉ All Rights Reserved by 2IIM.com - A Fermat Education Initiative.
Privacy Policy | Terms & Conditions
CATยฎ (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
Mobile: (91) 99626 48484 / 94459
38484
WhatsApp: WhatsApp Now
Email: info@2iim.com