Question

Queria saber o valor de n, por favor me expliquem

Answer 1

$Ola'~~~\mathbf{Yasmin} \\ \\ Seja~a~express\~ao: \\ \\ 2^{n+2}= 2^{n}+48 \\ \\ \underline{Resoluc\~ao~} \\ \\ 2^{n}. 2^{2}- 2^{n}=48~~--\ \textgreater \ fatorizamos~( 2^{n}~), seria \\ \\ 2^{n}( 2^{2}-1)=48 \\ \\ 2^{n}.(3)=48 ~~---\ \textgreater \ isolando~[ 2^{n}] \\ \\ 2^{n}= \frac{48}{3} \\ \\ 2^{n}=16 \\ \\ 2^{n}= 2^{4}~~---\ \textgreater \ bases~igual~expoente~se~iguala \\ \\ \boxed{\boxed{n=4 }}$


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