# CAT Quantitative Aptitude Questions | CAT Logarithms and Exponents

###### CAT Questions | Logarithms and Exponents | Logarithm - Inequalities

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?

1. 7
2. 6
3. 9
4. 12

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##### Method of solving this CAT Question from Logs and Exponents: Sum of N natural numbers comes as handy at times!

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?"

##### Hence, the answer is "7".

Choice A is the correct answer.

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