219 1) 7ˣ⁻² = 3²⁻ˣ;

1) 7ˣ⁻² = 3²⁻ˣ

$$7^{x-2} = 3^{2-x}$$

$$7^{x-2} = \frac{3^2}{3^x}$$

$$7^{x-2} = \frac{9}{3^x}$$

Прологарифмируем обе части:

$$(x-2)\log(7) = \log(9) - x\log(3)$$

$$x\log(7) - 2\log(7) = \log(9) - x\log(3)$$

$$x\log(7) + x\log(3) = \log(9) + 2\log(7)$$

$$x(\log(7) + \log(3)) = \log(9) + \log(49)$$

$$x = \frac{\log(9 \cdot 49)}{\log(7 \cdot 3)} = \frac{\log(441)}{\log(21)}$$

$$x = \frac{\log(21^2)}{\log(21)} = \frac{2 \log(21)}{\log(21)} = 2$$

Ответ: 2