Powers And Tetrations

Algebra Level 3

What is the sum of all integers $n$ satisfying

$\Large 2^n \times 2^n = 2^{2^n} \quad ?$

The answer is 3.

1 solution

Ayush G Rai
Sep 16, 2016

well we can re-write it as $2^{2n}=2^{2^{n}}\Rightarrow 2n=2^n.$ So The integers that satisfies $n$ are $1$ and $2.$
Therefore the sum of all integers $n=1+2=\boxed 3.$

How do you know that there are no integers other than 1 and 2 satisfying the property?

Anandmay Patel - 4 years, 9 months ago

To justify my statement,lets keep n>2 [First case]
plug in values for n in the equation 2n=2^n and you will notice that the right hand will always be greater than the left hand side.
Now keep n<1 [Second case]
plug in values for n in the equation 2n=2^n and you will notice that the right hand will always be greater than the left hand side.

Ayush G Rai - 4 years, 9 months ago

Understood.Thanks

Anandmay Patel - 4 years, 9 months ago

@Anandmay Patel – you are always welcome.!

Ayush G Rai - 4 years, 9 months ago

Powers And Tetrations

The answer is 3.

1 solution

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