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

1) log₃x * (5 - 2log₃x) = 3 5log₃x - 2log₃²x = 3 2log₃²x - 5log₃x + 3 = 0 log₃x = t 2t² - 5t + 3 =0 t₁ = 1 t₂ = [latex] \frac{3}{2} [/latex] log₃x = 1 x = 3 log₃x = [latex] \frac{3}{2} [/latex] x = [latex] \sqrt{27} [/latex] Ответ: 3 ; [latex] \sqrt{27} [/latex] 2) log₂²x + 3log₁/₂x + 2 =0    log₂²x + 3*[latex] \frac{ log_{2}x }{ log_{2} \frac{1}{2} } [/latex] + 2 = 0 log₂²x  - 3log₂x + 2 =0 log₂x = t t² - 3t + 2 =0 t₁ = 1 t₂ = 2 log₂x = 1 x = 2 log₂x = 2 x = 4 Ответ: 2; 4 3) (1/2log₃x - 6 )*log₉x = 4(2-log₉x) (1/2log₃x - 6) * [latex] \frac{ log_{3}x }{2} = 4(2- \frac{ log_{3}x }{2} )[/latex] [latex] \frac{ log_{3} ^{2}x }{4}- 3 log_{3}x = 8-2 log_{3}x [/latex] log₃x = t t² - 12t = 32 - 8t t² - 4t - 32 = 0 D₁ = 4+32=36 t₁ = 8 t₂ = -4 log₃x = 8 x = [latex] 3^{8} [/latex] log₃x = -4 x = [latex] 3^{-4} = \frac{1}{81} [/latex] 4) log₂x * log₃x = 4log₃2 [latex] \frac{ log_{3}x }{ log_{3}2 } * log_{3}x = 4 log_{3}2 [/latex] [latex] log_{3} ^{2}x = 4 log_{3} ^{2}2 [/latex] log₃x = 2log₃2              log₃x = -2log₃2 log₃x = log₃4                log₃x = log₃[latex] \frac{1}{4} [/latex] x=4                              x = [latex] \frac{1}{4} [/latex] 5) lg²x + 4 = 2*2*lgx lg²x - 4lgx + 4 = 0 lgx = t t² - 4t + 4=0 D₁ = 4-4=0 t = 2 lgx = 2 x = 100