# CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

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

The question is from Log and Exponents. A question on possible maximum value. We need to maximize the value of a - b under the given conditions. 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 5: $$frac{log_3{x-3}}{log_3{x-5}}\\$ < 0. If a, b are integers such that x = a, and x = b satisfy this inequation, find the maximum possible value of a – b. 1. 214 2. 216 3. 200 4. 203 ## 2IIM : Best Online CAT Coaching #### 2IIM's Online CAT CoachingGet CAT Last Mile Prep Course for 799 /-CAT Online Coaching ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2020Starts Sat, November 2nd, 2019 ### Explanatory Answer ##### Method of solving this CAT Question from Logs and Exponents: Simple inequalities questions appear exponentially tougher when Logarithms are thrown in. $\frac{log_3{x - 3}}{log_3{x - 5}}\\$ < 0 log3x = y => $\frac{y - 3}{y - 5}\\$ < 0 y ∈$3, 5)
3 < log3x < 5
27 < x < 243
Therefore max ( a – b) will be when a = 242 and b = 28. Therefore, max(a – b) = 214.

The question is "find the maximum possible value of a – b."

##### Hence, the answer is "214".

Choice A is the correct answer.

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