# CAT 2020 Question Paper | Quants Slot 3

###### CAT Previous Year Paper | CAT Quants Questions | Question 3

Logarithms is one of the most commonly tested topics in CAT exam. This topic plays a pivotal role in your CAT preparation. Questions from Logarithms have appeared consistently for several years in CAT exam. This question tests your understanding of the properties of Logarithms. If you're thorough with your fundamentals, then you're through. CAT Exam is known to test your fundamentals rather than high funda ideas. CAT Logarithms and Exponents is a favorite in CAT Exam, with every extra hour you log in for this topic, it becomes exponentially simpler.

Question 3 : Let loga30 = A, loga$$frac{5}{3}$ = -B and log2a = $\frac{1}{3}$, then log3a equals 1. $\frac{2}{A+B-3}$ 2. $\frac{A+B-3}{2}$ 3. $\frac{A+B}{2}$ - 3 4. $\frac{2}{A+B}$ - 3 ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer Let loga30 = A be equation 1. and loga$\frac{5}{3}$ = -B be equation 2. We are told that log2a = $\frac{1}{3}$ log2a = $\frac{1}{3}$ implies loga2 = 3 Dividing eqn$1) and eq(2) by loga2 = 3
We get; log230 = $$frac{A}{3}$ and log2$\frac{5}{3}$ = -$\frac{B}{3}$ log230 = log2$5 × 3 × 2)
$$frac{A}{3}$ = log25 + log23 + log22 $\frac{A}{3}$ = log25 + log23 + 1, let's call this equation 3 log2$\frac{5}{3}$ = log25 - log23 -$\frac{B}{3}$ = log25 - log23, let's call this equation 4 Solving equations 3 and 4 we get, log23 = $\frac{A+B-3}{6}$ Dividing this by log2a = $\frac{1}{3}$ we get, log2a = $\frac{A+B-3}{2}$ log2a = $\frac{A+B-3}{2}$ implies loga2 = $\frac{2}{A+B-3}$ The question is "Let loga30 = A, loga$\frac{5}{3}$ = -B and log2a = $\frac{1}{3}$, then log3a equals" ##### Hence, the answer is, "$\frac{2}{A+B-3}$" ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Prepare for CAT 2024 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram and @Anna nagar ###### Best CAT Coaching in Chennai Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Questions | CAT Quantitative Aptitude ## 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? Mobile:$91) 99626 48484 / 94459 38484
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