The question is from Log and Exponents. This question is about logarithm inequalities. We need to find out the value of x 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 13: 46+12+18+24+…+6x = (0.0625)-84, what is the value of x?
Take right side expression,
(0.0625)-84 = \\frac{1}{16}\\)-84
= (4-2)-84
= 4168
Take left side expression
46+12+18+24+…+6x = 46(1+2+3+4+x)
= 46 * 4(1+2+3+4+…+x)
= 46 * 4x(x+1)/2 (using the formula for sum of natural numbers from 1 to x)
Equating left and right side expresssions, we get 46 * 4x(x+1)/2 = 4168
Or 46 * 4x(x+1)/2 = 46*28
=> \\frac{x(x+1)}{2}\\) = 28
or x (x + 1) = 56
Solving for x we get, x = 7
The question is "what is the value of x?"
Choice A is the correct answer.
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