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: $-log_2 (5)$