CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

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

Video Explanation

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)) = 9^1/2 = 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.