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 $3^{2} < (- 3)^{x}$ .

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

_

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Solution

We need to find the value of x such that $3^{2} < (- 3)^{x}$
Now $(- 3)^{1} = - 3$
$(- 3)^{2} = - 3 \times - 3 = 9$

$(- 3)^{3} = - 3 \times - 3 \times - 3 = 27$

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, $3^{2} = 3 \times 3 = 9$

So, if $3^{2} < (- 3)^{x}$ , then x must be an even integer, since $(- 3)^{x}$ should be greater than 9.

Thus, x = 4, as $(- 3)^{2} = 9 = 3^{2}$

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Similar questions

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