CAT 2020 Question Paper | Quants Slot 3

This question is from logarithm and exponents. With every extra hour you log in for this topic, it becomes exponentially simpler. 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 11 : If a,b,c are non-zero and 14^a = 36^b = 84^c, then 6b($\frac{1}{c}$ - $\frac{1}{a}$) is equal to

Video Explanation

Explanatory Answer

Let 14^a = 36^b = 84^c = x

14^a = x
log₁₄x = a
log_x14 = $\frac{1}{a}$

36^b = x
log₃₆x = b

84^c = x
log₈₄x = c
log_x84 = $\frac{1}{c}$

$\frac{1}{c}$ - $\frac{1}{a}$ = log_x84 - log_x14 = log_x($\frac{84}{14}$ = log_x6
6 × b × ($\frac{1}{c}$ - $\frac{1}{a}$)
6 × log₃₆x × log_x6
6 × $\frac{log x}{log 36}$ × $\frac{log 6}{log x}$
6 × $\frac{log 6}{log 36}$
6 × log₃₆6
6 × $\frac{1}{2}$
3.

The question is "If a,b,c are non-zero and 14^a = 36^b = 84^c, then 6b($\frac{1}{c}$ - $\frac{1}{a}$) is equal to"

Hence, the answer is, "3"

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