Question

) Află n, dacă 2n + 2n+1+2n+2+ 2n+2 =120.​

Answer 1

Explicație pas cu pas:

${2}^{n} + {2}^{n + 1} + {2}^{n + 2} + {2}^{n + 3} = 120$

${2}^{n} \cdot (1 + 2 + {2}^{2} + {2}^{3}) = 120$

$15 \cdot {2}^{n} = 120 \\ {2}^{n} = 120 : 15$

${2}^{n} = 8 \iff {2}^{n} = {2}^{3} \\ \implies n = 3$