Question

Without actually calculation,find which is greater 31 11 or 17 14

Answer 1

They key to this problem is 17 x 2=34 and 34>31
31¹¹<34¹¹
34¹¹=(17 x 2)¹¹=17¹¹ x 2¹¹= 17¹¹ x 2⁴ x 2⁴ x 2³
 17¹¹ x 2⁴ x 2⁴ x 2³< 17¹¹ x 17 x 17 x 17
17¹¹ x 17 x 17 x 17=17¹⁴
therefore 31¹¹<17¹⁴

Answer 2

17¹⁴ is greater than 31¹¹

GIVEN

Numbers; 31¹¹ 17¹⁴

TO FIND

Which of the given number is greater.

SOLUTION

We can simply solve the above problem as follows;

We are given a number,

31¹¹ and 17¹⁴

Now,

(17 × 2)¹⁴ = (34)¹⁴

We know that,

34 > 31

Therefore,

17 x 2=34 and 34>31

31¹¹<34¹¹

34¹¹=(17 x 2)¹¹=17¹¹ x 2¹¹= 17¹¹ x 2⁴ x 2⁴ x 2³

17¹¹ x 2⁴ x 2⁴ x 2³< 17¹¹ x 17 x 17 x 17

17¹¹ x 17 x 17 x 17=17¹⁴

Since,

31¹¹ is smaller than 34¹¹

And,

34¹¹ = 17¹⁴

Hence, 31¹¹ < 17¹⁴

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