Question

0.2=2^n. Знайти n. Даю 50б

Answer 1

$\frac{1}{5} = 2^n$

log₂0.2 = log₂2ⁿ
log₂0.2 = n

n ≈ -2.32

Answer 2

$2^n=0.2 \Rightarrow 2^n=\cfrac{2}{10} = \cfrac{1}{5} = 5^{-1} \Rightarrow 2^n = 5^{-1}\\\\ n = \log_2(5^{-1})=-\log_2(5)$

Ответ: $-\log_2 (5)$