CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

CAT Questions

The question is from Log and Exponents. We can solve this easily using log identities. We need to find out the value of n from the given equation. 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 9: log₂ 4 * log₄ 8 * log₈ 16 * ……………nth term = 49, what is the value of n?

1. 49
2. 48
3. 34
4. 24

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Explanatory Answer

Method of solving this CAT Question from Logs and Exponents: Application of Basic Identities of Logarithms!

First, the nth term of L.H.S need to be defined by observing the pattern :-
It is log_(2ⁿ) 2∙2ⁿ
Given,
log₂ 4 * log₄ 8 * log₈ 16 * ……………log_(2ⁿ) 2 ∙ 2 ⁿ = 49
Whenever solving a logarithm equation, generally one should approach towards making the base same.

Making the base 2:-
log₂ 4 * \\frac {log_2{8}}{log_2{4}}\\) * \\frac {log_2{16}}{log_2{8}}\\) * ....... \\frac {log_2{2∙2^n}}{log_2{2^n}}\\)
log₂ 2∙2ⁿ = 49
log₂ 2 + log₍₂₎ 2ⁿ = 49
1 + n = 49
n = 48

The question is "what is the value of n?"

Hence, the answer is "48".

Choice B is the correct answer.