Find $n$: $2^{n} + 2^{n} = 64$.

Find $n$: $2^{n} + 2^{n} = 64$.
  1. $5$
  2. $6$
  3. $32$
  4. $\log_{2} 32$

Solution

$2 \cdot 2^{n} = 2^{n+1} = 64 = 2^{6}$, so $n + 1 = 6 \Rightarrow n = 5$.

Asked in: IMO

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