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CAT Previous Year Paper | CAT Quants Questions | Question 11

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 14a = 36b = 84c, then 6b(\\frac{1}{c}) - \\frac{1}{a})) is equal to


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Explanatory Answer

Let 14a = 36b = 84c = x

14a = x
log14x = a
logx14 = \\frac{1}{a})

36b = x
log36x = b

84c = x
log84x = c
logx84 = \\frac{1}{c})

\\frac{1}{c}) - \\frac{1}{a}) = logx84 - logx14 = logx(\\frac{84}{14}) = logx6
6 × b × (\\frac{1}{c}) - \\frac{1}{a}))
6 × log36x × logx6
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 14a = 36b = 84c, then 6b(\\frac{1}{c}) - \\frac{1}{a})) is equal to"

Hence, the answer is, "3"

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