Вычислите: (P4 × C9^4)/ A9^4

Question

Алгебра: Вычислите: (P4 × C9^4)/ A9^4

Рэйн0165 · Accepted Answer

Log₂₄54, если log(2)3=a

log₂₄54 = log₂₄ 2*27= log₂₄ 2+ log₂₄ 27= log₂₄ 2+ log₂₄ 3³=  log₂₄ 2+ 3log₂₄ 3 =

1 3 1 3 1 3
= ----------- + ---------- = --------------- + -------------- = ------------------- +------------------
  log₂ 24 log₃24 log₂ 8*3 log₃3*8 log₂2³+log₂ 3   log₃3+ log₃2³

1 3
= -------------- + ------------- =
3+log₂ 3 1+3log₃2

1 3
= -------------- + ------------- =
3+log₂ 3 1+3/log₂ 3

   1    3 log₂ 3 1+3log₂ 3 1+3a
= -------------- + ----------------- = --------------- ; при log₂3 =a --------------
3+log₂ 3 (log₂3 +3) 3+log₂ 3 3+a

Вычислите log(24)54, если log(2)3=a

MOGZ ответил

Вычислите:
(P4 × C9^4)/ A9^4