3. Let the set $A=\left\{x \in \boldsymbol{N} \mid 2^{n}<x \leq 2^{n+1}, n \in \boldsymbol{N}\right\}$

( 4p ) a) How many elements does the set $A$ have in the case $n=2014$.

( 3 p ) b) Determine the number $n$ for which the set $A$ has 128 elements
3. a ) $n=2014 \quad 2^{2014}<x \leq 2^{2015}$

$$
\Rightarrow A=\left\{2^{2014}+1,2^{2014}+2, \ldots, 2^{2015}\right\}
$$

$\operatorname{Card} A=\left(2^{2015}-2^{2014}\right)=2^{2014}$

b ) Card $\mathrm{A}=\left(2^{n+1}-2^{n}\right)=2^{n}\left(2^{1}-1\right)=2^{n}$

If $2^{n}=128 \Rightarrow 2^{n}=2^{7}$, so $n=7$