# CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

###### CAT Questions | Logarithms and Exponents | Logarithm - Different bases CAT Questions

The question is from Log and Exponents. This questions is about Logarithm - Different bases. We need to find out the value of log in terms of a and b based on given another two log values. 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 6: log5x = a (This should be read as log X to the base 5 equals a) log20x = b. What is logx10?

1. $$frac{a + b}{2ab}\\$ 2.$a + b) * 2ab
3. $$frac{2ab}{a + b}\\$ 4. $\frac{a + b}{2}\\$ ## 🎉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. Given, log5x = a log20x = b logx5 = $\frac{1}{a}\\$ logx20 = $\frac{1}{b}\\$ logx$\frac{100}{5}\\$ = $\frac{1}{b}\\$ logx100 - logn5 = $\frac{1}{b}\\$ => 2logx10 - $\frac{1}{a}\\$ = $\frac{1}{b}\\$ logx10 = $\frac{1}{2}\\$$$$frac{1}{a}\\$ + $\frac{1}{b}\\$) logx10 = $\frac{a + b}{2ab}\\$ The question is "What is logx10?" ##### Hence, the answer is "$\frac{a + b}{2ab}\\$". Choice A 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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