Как сможете 1) log3.2 (2-x) = log3.2 (3x+6) 2) log0.8 (1+2x) = log0.8 (4x-10) 3) log2 (x-6)+ log2 (x-8) = 3 4) log8 (x-2) - log8 (x-3) = 1/3 1) lg (5-x) = 1/3lg (35-x^3) 2) log2 x-5/x+5 + log2 (x+5) = 0 3) log2 (3x-6) - 1 = log2 (9x-19) 1)log7 (x-2) + log7 (x+2) = log7 (4x+41) 2) log4 (x+1) - log4 (1-x) = log4 (2x+3) 3) log4 (x+3) - log4 (x-1) = 2 - log4 8 4) lg (x-1) + lg (x+1) = 3lg2 + lg (x-2) 1) 2 log3 (x-2) + log3 (x-4)^2 = 0 2) 2lgx - lg4 + lg (5-x^2) = 0 3) lg [x(x+9)] + lg x+9/x = 0

1) log₃.₂ (2-x) = log₃.₂ (3x+6) 2-x = 3x+6 -4x = 4 x = -1 ответ: -1 2) log₀.₈(1+2x) = log₀.₈ (4x-10) 1+2x = 4x-10 -2x = -11 x = 5.5 ответ: 5,5 3) log₂ (x-6) + log₂ (x-8) = 3 одз: x-6> 0           x-8> 0 log₂ ((x-6)(x-8)) = log₂8 (x-6)(x-8) = 8 x² - 8x - 6x + 48 = 8 x² - 14x + 40 = 0 d₁ = 49-40 = 9 x₁ = 7+3 = 10 x₂ = 7-3 = 4  не удов. одз ответ: 10 4) log₈ (x-2) - log₈ (x-3) = 1/3 одз: x-2> 0           x-3> 0 log₈ = log₈2 x-2 = 2x - 6 -x = -4 x = 4 ответ: 4 1) lg (5-x) = 1/3 lg(35-x³) одз: 5-x> 0           35-x³ > 0 lg (5-x) = lg 5-x = (5-x)³ = 35-x³ 125 - 3*25*x + 3*5*x² - x³ = 35-x³ 125 - 75x + 15x² - 35 = 0 15x² - 75x +90 = 0 x² - 5x + 6 = 0 d = 25 - 24 = 1 x₁ = (5+1)/2 = 3 x₂ = (5-1) / 2 =2 ответ: 3; 2 2) log₂ + log₂ (x+5) = 0 одз: x-5> 0           x+5> 0 log₂ = 0 log₂ (x-5) = 0 x-5 = 1 x = 6 ответ: 6 3) log₂ (3x-6) - 1 = log₂ (9x-19) log₂ (3x-6) = log₂ (9x-19) + 1 log₂ (3x-6) = log₂ (9x-19) + log₂2 log₂ (3x-6) = log₂ ((9x-19)*2) 3x-6 = 18x - 38 15x = 32 x = ответ: 32/15 1) log₇ (x-2) +log₇(x+2) = log₇ (4x+41) одз: x-2> 0           x+2> 0           4x+41 > 0 log₇ ((x-2)(x+2)) = log₇ (4x+41) (x-2)(x+2) = 4x+41 x² - 4  = 4x +41 x² - 4x - 45 = 0 d₁ = 4 + 45 = 49 x₁ = 2+7 = 9 x₂ = 2-7 = -5 не удов. одз ответ: 9 2) log₄ (x+1) - log₄(1-x) = log₄ (2x+3) одз: x+1> 0           1-x> 0           2x+3> 0 log₄ (x+1) = log₄(2x+3) + log₄ (1-x) log₄ (x+1) = log₄ ((2x+3)(1-x)) x+1 = 2x - 2x² + 3 - 3x 2x² + 2x - 2 = 0 x² + x - 1 = 0 d = 1 + 4 = 5 x₁ = (-1+√5)/2 x₂ = (-1-√5) / 2  не удов.одз ответ: (-1+√5) / 2 3) log₄ (x+3) - log₄  (x-1) = 2- log₄8 log₄ log₄16 - log₄8 log₄ = log₄2   ( x+3 = 2x - 2 -x = -5 x = 5 ответ: 5 4) lg (x-1) + lg (x+1) = 3lg2 + lg (x-2) lg ((x-1)(x+1)) = lg8 + lg (x-2) lg (x² - 1) = lg (8(x-2)) x² - 1 = 8x- 16 x² - 8x + 15 = 0 d₁ = 16 - 15 = 1 x₁ = 4 + 1 =5 x₂ = 4-1 = 3 ответ: 5; 3 1) 2log₃(x-2) + log₃ (x-4)² = 0 одз:   x-2> 0             x-4> 0 2log₃ (x-2)+ 2log₃ (x-4) = 0 2 (log₃(x-2) + log₃ (x-4)) = 0 log₃ ((x-2)(x-4)) = 0 (x-2)(x-4) = 1 x² - 4x - 2x + 8 = 1 x² - 6x + 7 = 0 d₁ = 9 - 7 = 2 x₁ = 3 + √2 x₂ = 3 -√2 не удов. одз ответ; 3+√2 2) 2lgx  - lg4 + lg (5-x²) = 0 одз: x> 0           5-x² > 0 lgx² + lg (5-x²) = lg4 lg (x² (5-x²)) = lg4 x² (5-x²) = 4 5x² - x⁴ = 4 5x² - x⁴ - 4 = 0 x⁴ - 5x² + 4 =0 x² = t ; t> 0 t² - 5t + 4 = 0 t₁ = 1 t₂ = 4 x² = 1          x² = 4 x₁ = 1        x₁ = 2 x₂ = -1      x₂ = -2 корни -1 и -2 не удов. одз ответ: 1; 2