![9^x*(\frac{1}{3})^{2-3x}=\sqrt{27^x}*\sqrt[3]{81^{x+3}}\\(3^2)^x*(3^{-1})^{2-3x}=((3^3)^x)^\frac{1}{2}*((3^4)^{x+3})^\frac{1}{3}\\3^{2x}*3^{3x-2}=3^{\frac{3x}{2}}*3^{\frac{4(x+3)}{3}}\\3^{2x+3x-2}=3^{\frac{3x}{2}+\frac{4(x+3)}{3}}\\5x-2=\frac{3x}{2}+\frac{4(x+3)}{3}\ \ \ \ \ \ \ |*6\\30x-12=9x+8x+24\\13x=36\\x=\frac{36}{13}](https://tex.z-dn.net/?f=9%5Ex%2A%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B2-3x%7D%3D%5Csqrt%7B27%5Ex%7D%2A%5Csqrt%5B3%5D%7B81%5E%7Bx%2B3%7D%7D%5C%5C%283%5E2%29%5Ex%2A%283%5E%7B-1%7D%29%5E%7B2-3x%7D%3D%28%283%5E3%29%5Ex%29%5E%5Cfrac%7B1%7D%7B2%7D%2A%28%283%5E4%29%5E%7Bx%2B3%7D%29%5E%5Cfrac%7B1%7D%7B3%7D%5C%5C3%5E%7B2x%7D%2A3%5E%7B3x-2%7D%3D3%5E%7B%5Cfrac%7B3x%7D%7B2%7D%7D%2A3%5E%7B%5Cfrac%7B4%28x%2B3%29%7D%7B3%7D%7D%5C%5C3%5E%7B2x%2B3x-2%7D%3D3%5E%7B%5Cfrac%7B3x%7D%7B2%7D%2B%5Cfrac%7B4%28x%2B3%29%7D%7B3%7D%7D%5C%5C5x-2%3D%5Cfrac%7B3x%7D%7B2%7D%2B%5Cfrac%7B4%28x%2B3%29%7D%7B3%7D%5C+%5C+%5C+%5C+%5C+%5C+%5C+%7C%2A6%5C%5C30x-12%3D9x%2B8x%2B24%5C%5C13x%3D36%5C%5Cx%3D%5Cfrac%7B36%7D%7B13%7D "9^x*(\frac{1}{3})^{2-3x}=\sqrt{27^x}*\sqrt[3]{81^{x+3}}\\(3^2)^x*(3^{-1})^{2-3x}=((3^3)^x)^\frac{1}{2}*((3^4)^{x+3})^\frac{1}{3}\\3^{2x}*3^{3x-2}=3^{\frac{3x}{2}}*3^{\frac{4(x+3)}{3}}\\3^{2x+3x-2}=3^{\frac{3x}{2}+\frac{4(x+3)}{3}}\\5x-2=\frac{3x}{2}+\frac{4(x+3)}{3}\ \ \ \ \ \ \ |*6\\30x-12=9x+8x+24\\13x=36\\x=\frac{36}{13}")
0\\\frac{2}{t}-8t-15=0\ \ \ \ \ \ \ \ |*t\\2-8t^2-15t=0\\8t^2+15t-2=0\\D=225+64=289=17^2\\t_1=\frac{-15+17}{16}=\frac{2}{16}=\frac{1}{8}\\t_2=\frac{-15-17}{16}=-\frac{32}{16}=-2" alt="2^{1-x}-2^{3+x}-15=0\\2^1*2^{-x}-2^3*2^x-15=0\\\frac{2}{2^x}-8*2^x-15=0\\\\2^x=t,\ t>0\\\frac{2}{t}-8t-15=0\ \ \ \ \ \ \ \ |*t\\2-8t^2-15t=0\\8t^2+15t-2=0\\D=225+64=289=17^2\\t_1=\frac{-15+17}{16}=\frac{2}{16}=\frac{1}{8}\\t_2=\frac{-15-17}{16}=-\frac{32}{16}=-2" align="absmiddle" class="latex-formula">
t₂∉t>0
