# CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

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

The question is from Log and Exponents. A question that combines logarithm with Algebra. We need to find out a logarithm in terms of a and b. 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 4: If log1227 = a, log916 = b, find log8108.

1. $$frac{2$a + 3$}{3b}$ 2. $\frac{2$a + 3$}{3a}$ 3. $\frac{2$b + 3$}{3a}$ 4. $\frac{2$b + 3$}{3b}$ ## 🎉Get Upto ₹6,000 off on our CAT 2024 and IPM 2024/25 courses! Valid till 1st December 2023.★ Register now ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from Logs and Exponents: 2 can be expressed as a power of 3, 3 can be expressed as a power of 5. Do not live in the world that has only rational numbers; it is irrational to do that. log8108 = log8$4 * 27)
log8108 = log84 + log827
=> log84 = $$frac{2}{3}\\$ log827 = $\frac{log_16{27}}{log_16{8}}\\$ log827 = $\frac{log_16{27}}{3/4}\\$ log827 = $\frac{4}{3}\\$ log1627 log827 = $\frac{4}{3}\\$ $\frac{log_9{27}}{log_9{16}}\\$ log827 = $\frac{4}{3}\\$ $\frac{\\frac{3}{2}}{log_9{16}}\\$ log827 = 2 * log169 log916 = b log169 = $\frac{1}{b}\\$ log827 = $\frac{2}{b}\\$ log8108 = $\frac{2}{3}\\$ + $\frac{2}{b}\\$ = 2$$$frac{1}{3}\\$ + $\frac{1}{b}\\$) = $\frac{2$b + 3$}{3b}$. The question is "find log8108." ##### Hence, the answer is "$\frac{2$b + 3$}{3b}$". Choice D 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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