# CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

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

The question is from Log and Exponents. This ia about base of a logarithm. We need to find out the base of a logarithm. 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 2: log9 (3log2 (1 + log3 (1 + 2log2x))) = $$frac{1}{2}\\$. Find x. 1. 4 2. $\frac{1}{2}\\$ 3. 1 4. 2 ## 🎉Get Upto ₹6,000 off on our CAT 2024 and IPM 2024/25 courses! Valid till 1st December 2023.★ Register now ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from Logs and Exponents: Its amazing how many questions one can solve in the exam knowing only the very basics. log9$3log2 (1 + log3 (1 + 2log2x)) = $$frac{1}{2}\\$ 3log2$1 + log3(1 + 2log2x)) = 91/2 = 3
log2(1 + log3(1 + 2log2x) = 1
1 + log3(1 + 2log2x) = 2
log3(1 + 2log2x) = 1
1 + 2log2x = 3
2log2x = 2
log2x = 1
x = 2

The question is "Find x."

##### Hence, the answer is "2".

Choice D is the correct answer.

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