Question

Помогите а=log50(40). Выразить log5(2) через а​

Answer 1

$a = log_{50}40 = \frac{ln40}{ln50} = \frac{3ln2 + ln5}{ln2 + 2ln5} = \frac{3log_52 + 1}{log_52 + 2} => a*log_52 + 2a = 3log_52 + 1 => log_52(a-3) = 1 - 2a => log_52 = \frac{1-2a}{a-3}$