# 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 x from the given 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 7: log3x + logx3 = $$frac{17}{4}\\$. Find the value of x. 1. 34 2. 31/4 3. 34 or 31/4 4. 31/3 ## 🎉Get Upto ₹6,000 off on our CAT 2024 and IPM 2024/25 courses! Valid till 1st December 2023.★ Register now ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from Logs and Exponents: When we change the base, Log questions become far tougher. log3x + logx3 = $\frac{17}{4}\\$ Let y = log3x We know that logx3 = $\frac{1}{log_3{x}}\\$ Hence logx3 = $\frac{1}{y}\\$ Thus the equation can be written as y + $\frac{1}{y}\\$ = $\frac{17}{4}\\$ 4y2 + 4 = 17y 4y2 + 4 - 17y = 0 Solving the above equation we get y = 4 or $\frac{1}{4}\\$ If y = 4 log3x = 4 Then x = 34 If y = $\frac{1}{4}\\$ log3x = $\frac{1}{4}\\$ Then x = 31/4 The question is "Find the value of x." ##### Hence, the answer is "34 or 31/4". Choice C is the correct answer. ###### 🎉Get Upto ₹6,000 off on our CAT 2024 and IPM 2024/25 courses! Valid till 1st December 2023. ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2023 Classroom Batches Starting Now! @Gopalapuram ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## 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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