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].

_

Open in App

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 $(- 3)^{2} = 9 = 3^{2}$

Suggest Corrections

Similar questions

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].

___

Having entered the passcode correctly, Tom got his mission. He needs to fight an enemy combatant and get information about the next clue. Tom found the room where the combatant was, but to enter the room, he needed another passcode.The passcode is the answer to the following display:

“The lock thinks that 0.36 = 3 $\times$ $10^{a}$ + 6 $\times$ $10^{b}$ and the passcode is the value (a $\times$ b)”

What is the passcode that Tom has to enter? ______ [Enter a numerical value]

___

After getting the code, Tom got past the commando to enter the structure. This was the final level.He was supposed to find the chip which contained military grade secrets and retrieve it. After Tom retrieves the chip, he was supposed to destroy the entire structure and leave no traces of it.

He had to fix a certain amount of C4 explosives on all the 4 walls of the structure.He had to choose one pair of equal amounts of C4 on two walls.

There was C4 explosive material packed in 4 boxes and the amount of C4 inside each box was specified in the “power” notation. Select the options which have equal amounts of C4 –

Tom now had access to the ammunition [ammo]. He now had to load a correct amount of ammo to shoot the combatant. The gun calculated the amount of ammo to be loaded and displayed the following to Tom –

“There are 27 bullets that can be fired in each roundand 64 rounds are available, which means $27 \times 64 = 2^{x} \times 3^{y}$ bullets can be shot”

The gun can be activated digitally by entering another passcode, which is the numerical value of (x-y).

What is the passcode that Tom has to enter? ______ [Enter a numerical value]

___

After completely filling the jet pack, Tom flew to the apex of the structure and retrieved the chip. He left the structure and now he had to demolish the entire building. To do this, he had a remote – on which, he had to touch all the equal valued buttons, as given in the given options. The game would be over once the building is demolished and Tom would win.

Choose the option which Tom should touch to demolish the structure:

Join BYJU'S Learning Program