Question

Найдите а по его логарифму. 1) log2 a = 4log2 √3 2) log3 a = (log3)2 + (log9)3 3) loga a = 3loga7 - 0,25loga3 4) loga a = 5loga3 + 1/4loga5 + 3loga7 5) loga a = 2/3loga √2 + 5/6 loga2^6 6) log2 a = log2 ((log4)5) - (log0,25)10)

Answer 1

1) log₂ A = 4log₂√3,⇒log₂ A = log₂√3⁴, ⇒ log₂ A = log₂√81,⇒log₂ A = log₂9,
       А = 9
2) log₃ A = log₃2 + log₉3⇒log₃ A = log₃2 + log₃3/log₃9,⇒
log₃ A = log₃2 + l/2, ⇒log₃ A = log₃2 + log₃(√3).
А = 2√3
3) loga A = 3loga7 - 0,25loga3
     А = 7³/⁴√3
4) loga A = 5loga3 + 1/4loga5 + 3loga7 
     А = 3⁵ * ⁴√5 * 7³
5) loga A = 2/3loga √2 + 5/6 loga2^6
       А = ∛а² *2⁵
6) log2 A = log2 ((log4)5) - (log0,25)10), 
        A = log₄5 - log₁/₄10 = log₄5 +log₄10 = log₄50