Решить неравенства: 1) log3 x * (5 - 2 log3 x) = - вопрос №2230922135233222312 от захро2007 22.10.2020 18:09

Question

Алгебра: Решить неравенства: 1) log3 x * (5 - 2 log3 x) = 3 2) (log2 x)^2 + 3 log1/2 x + 2 = 0 3) (1/2log3 x - 6) * log9 x = 4 (2 - log9 x) 4)log2 x * log3 x = 4 log3 2 5)lg x + 4 = 2 lg 100 lg x

захро2007 · Answer

1) log₃x * (5 - 2log₃x) = 35log₃x - 2log₃²x = 32log₃²x - 5log₃x + 3 = 0log₃x = t2t² - 5t + 3 =0t₁ = 1t₂ = log₃x = 1x = 3log₃x = x = ответ: 3 ; 2) log₂²x + 3log₁/₂x + 2 =0   log₂²x + 3* + 2 = 0log₂²x  - 3log₂x + 2 =0log₂x = tt² - 3t + 2 =0t₁ = 1t₂ = 2log₂x = 1x = 2log₂x = 2x = 4ответ: 2; 43) (1/2log₃x - 6 )*log₉x = 4(2-log₉x)(1/2log₃x - 6) * log₃x = tt² - 12t = 32 - 8tt² - 4t - 32 = 0D₁ = 4+32=36t₁ = 8t₂ = -4log₃x = 8x = log₃x = -4x = 4) log₂x * log₃x = 4log₃2log₃x = 2log₃2              log₃x = -2log₃2log₃x...