Question

Equação exponencial
(2^5)^(x-3)=1024

Answer 1

Resposta:

x=5

Explicação passo a passo:

$\displaystyle (2^5)^{(x-3)}=1024$

Decompor 1024:

1024 | 2

512 | 2

256 | 2

128 | 2

64 | 2

32 | 2

16 | 2

8 | 2

4 | 2

2 | 2

1 | 1

1024 = 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 = 2¹⁰

$\displaystyle (2^5)^{(x-3)}=1024\\\\ (2^5)^{(x-3)}=2^{10}\\\\5(x-3)=10\\\\x-3=\frac{10}{5} \\\\x-3=2\\\\x=2+3\\\\x=5$