# CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

###### CAT Questions | Logarithms and Exponents | Logarithm - Identities
CAT Questions

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: logxy + logyx2 = 3. Find logxy3.

1. 4
2. 3
3. 31/2
4. 31/16

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### Explanatory Answer

##### Method of solving this CAT Question from Logs and Exponents: Application of Basic Identities!!

logxy + logyx2 = 3
Let a = logxy
logx3 = $$frac{1}{log_3{x}}\\$ logyx2 = 2logyx We know that logyx = $\frac{1}{log_x{y}}\\$ Hence form above logyx = $\frac{1}{a}\\$ Now rewritting the equation logxy + logyx2 = 3 Using a we get a + $\frac{2}{a}\\$ = 3 i.e., a2 - 3a + 2 = 0 Solving we get a = 2 or 1 If a = 2, Then logxy = 2 and logyx3 = 3 logxy = 3 * 2 = 6 Or If a = 1, Then logxy = 1 and logyx3 = 3 logxy = 3 * 1 = 3 The question is "Find logxy3." ##### Hence, the answer is "3". Choice B is the correct answer. ###### Best Online CAT Preparation Miles ahead of others Signup to Try ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 35,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in ChennaiRegister Online, get Rs 7000/- off Attend a Demo Class ## CAT Preparation Online | CAT Arithmetic Videos On YouTube #### Other useful sources for Arithmetic Question | Logarithms and Exponents Sample Questions ##### 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
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