11 класс. Уравнения. Задание на картинке. 40 баллов.

Не пишу исходные. [latex]( 3^{x-3} ) ^{x+4} = 3^{x-3} log(3)(x - 3)(x + 4) = log(3)(3 - x) log(3)x^2 + log(3)x - 12log(3) = log(3)(3 - x) log(3)x^2 + log(3)x - 12log(3) = 3log(3) - log(3)x log(3)x^2 + 2log(3)x - 15 log(3) = 0 log(3)(x - 3)(x + 5) = 0 x - 3 = 0 ; x + 5 = 0 x1 = 3 ; x2 = - 5[/latex] [latex] \frac{7}{4} = 7 * 2^{x^2-x-4} [/latex] [latex] 2^{x^2-x-4} = \frac{1}{4} x^2 - x - 4 = - 2 x^2 - x = 2[/latex] [latex]x^2 - x + \frac{1}{4} = \frac{9}{4} [/latex] [latex](x - \frac{1}{2} )^2 = \frac{9}{4} [/latex] [latex]x - \frac{1}{2} = 1,5 ; x - \frac{1}{2} = - 1,5 x1 = 2 ; x2 = -1[/latex]

[latex](3^{x-3})^{x+4}=( \frac{1}{3})^{3x-1} \\ 3^{x^2+x-12}=3^{-3x+1} \\ x^2+x-12=-3x+1 \\ x^2+4x-13=0 \\ \Delta=16+4*13=16+52=68=4*17 \\ x_1= \frac{-4-2 \sqrt{17} }{2} =-2- \sqrt{17} \\ x_2=-2+ \sqrt{17} \\ [/latex] [latex]2^{x+2}+2^{x+3}+2^{x+4}=7*2^{x^2} \\ 2^x(4+8+16)=7*2^{x^2} \\ 28*2^x=7*2^{x^2} \\ 4*2^x=2^{x^2} \\ 2^{x+2}=2^{x^2} \\ x^2=x+2 \\ x^2-x-2=0 \\ \Delta=1+8=9=3^2 \\ x_1= \frac{1-3}{2}=-1 \\ x_2= \frac{1+3}{2}=2 \\ [/latex]