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Question

With sufficient ammo loaded, Tom managed to overpower his combatant and got the next clue and exited The Architecture.

Following the clue, Tom reached a particular structure called Exponere Quattuor. He had to go inside this structure for which he had to get past the entry.A commando was guarding the entry. Tom got a message from his spies that the only way to get past the commando is to give him the code which was – the minimum value of x (integer) for which 32<(3)x.

The code Tom gave was ____  [Enter a numerical value].


___


Solution

We need to find the value of x such that 32<(3)x
Now (3)1=3
(3)2=3×3=9

(3)3=3×3×3=27
 
So when the exponent is odd, the value of the power will be negative. When the exponent is even, the value of the power is positive

Now, 32=3×3=9

So, if 32<(3)x, then x must be an even integer, since (3)x should be greater than 9.

Thus, x = 4, as (3)2=9=32

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