250 1) 1,5⋅5ˣ⁻⁷ = (2/3)ˣ⁺¹;

1) 1,5⋅5ˣ⁻⁷ = (2/3)ˣ⁺¹

$$ \frac{3}{2} \cdot 5^{x-7} = \left(\frac{2}{3}\right)^{x+1} $$

$$ \frac{3}{2} \cdot 5^{x-7} = \frac{2^{x+1}}{3^{x+1}} $$

$$ 3^{x+2} = 2^{x+2} \cdot 5^{7-x} $$

$$ \left( \frac{3}{2} \right)^{x+2} = 5^{7-x} $$

$$ (x+2) \ln(3/2) = (7-x) \ln 5 $$

$$ x \ln(3/2) + 2\ln(3/2) = 7\ln 5 - x\ln 5 $$

$$ x (\ln(3/2) + \ln 5) = 7\ln 5 - 2\ln(3/2) $$

$$ x = \frac{7\ln 5 - 2\ln(3/2)}{\ln(3/2) + \ln 5} $$

$$ x = \frac{\ln 5^7 - \ln (3/2)^2}{\ln(3/2) \cdot 5} = \frac{\ln \frac{5^7}{(3/2)^2}}{\ln \frac{15}{2}} $$

$$ x = \frac{\ln \frac{5^7 \cdot 4}{9}}{\ln \frac{15}{2}} $$

$$ x = \frac{\ln \frac{625000}{9}}{\ln \frac{15}{2}} $$

Ответ: $$x = \frac{\ln \frac{625000}{9}}{\ln \frac{15}{2}} $$