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Question 13 : The smallest integer n for which 4ⁿ ＞ 17¹⁹ holds, is closest to

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Explanatory Answer

Method of solving this CAT Question from Number theory and Inequalities

Given that 4ⁿ > 17¹⁹
The smallest integer n for which 4ⁿ > 17¹⁹ holds has to be found 4ⁿ > 17¹⁹ can be also written as (4²)^{\\frac{n}{2})} > 17¹⁹
16^{\\frac{n}{2})} > 17¹⁹
We can assume n = 19, 16¹⁹ cannot be greater than 17¹⁹
16^{\\frac{38}{2})} cannot be greater than 17¹⁹ so n cannot be 38
And similarly n cannot be less than 38 so we can eliminate the options less than 38 and so the only possible value n could take is 39