1.
a) 2*9ˣ - 17*3ˣ = 9
2*3²ˣ - 17*3ˣ - 9 = 0
3ˣ = m одз: m > 0
2m² - 17m - 9 = 0 D = b²-4ac = 289+72 = 361 = 19²
m₁ = (-b+√D)/2a = (17+19):4 = 9
m₂ = (-b-√D)/2a = (17-19):4 = -0,5 - не удовлетворяет одз.
3ˣ = 9
3ˣ = 3²
х = 2
Ответ: {2}
б) 3ˣ⁻² - 3ˣ⁻³ = 6
3ˣ: 9 - 3ˣ : 27 = 6
3*3ˣ: 27 - 3ˣ: 27 = 6
2*3ˣ: 27 = 6
3ˣ = 81
3ˣ = 3⁴
x = 4
Ответ: {4}
в)
![\displaystyle ( \frac{1}{5 \sqrt{5} })^{x}= \sqrt[3]{5} \\ \\ (5 \sqrt{5})^{-x}=5^{1/3} \\ \\ (5^{3/2})^{-x}=5^{1/3} \\ \\ 5^{-3x/2}=5^{1/3} \\ \\ - \frac{3x}{2}= \frac{1}{3} \\ \\ -9x=2 \\ \\ x=- \frac{2}{9}](https://tex.z-dn.net/?f=%5Cdisplaystyle+%28+%5Cfrac%7B1%7D%7B5+%5Csqrt%7B5%7D+%7D%29%5E%7Bx%7D%3D+%5Csqrt%5B3%5D%7B5%7D+%5C%5C++%5C%5C+%285+%5Csqrt%7B5%7D%29%5E%7B-x%7D%3D5%5E%7B1%2F3%7D+%5C%5C++%5C%5C+%285%5E%7B3%2F2%7D%29%5E%7B-x%7D%3D5%5E%7B1%2F3%7D+%5C%5C++%5C%5C+5%5E%7B-3x%2F2%7D%3D5%5E%7B1%2F3%7D+%5C%5C++%5C%5C+-+%5Cfrac%7B3x%7D%7B2%7D%3D+%5Cfrac%7B1%7D%7B3%7D+%5C%5C++%5C%5C+-9x%3D2+%5C%5C+%5C%5C++x%3D-++%5Cfrac%7B2%7D%7B9%7D++++++ "\displaystyle ( \frac{1}{5 \sqrt{5} })^{x}= \sqrt[3]{5} \\ \\ (5 \sqrt{5})^{-x}=5^{1/3} \\ \\ (5^{3/2})^{-x}=5^{1/3} \\ \\ 5^{-3x/2}=5^{1/3} \\ \\ - \frac{3x}{2}= \frac{1}{3} \\ \\ -9x=2 \\ \\ x=- \frac{2}{9}")
Ответ: {-2/9}