4) 5ˣ⁺¹ + 3⋅5ˣ⁻¹ - 6⋅5ˣ + 10 = 0.

4) $$ 5^{x+1} + 3 \cdot 5^{x-1} - 6 \cdot 5^x + 10 = 0 $$

$$ 5 \cdot 5^x + \frac{3}{5} \cdot 5^x - 6 \cdot 5^x + 10 = 0 $$

$$ 5^x \left( 5 + \frac{3}{5} - 6 \right) + 10 = 0 $$

$$ 5^x \left( -1 + \frac{3}{5} \right) + 10 = 0 $$

$$ - \frac{2}{5} \cdot 5^x + 10 = 0 $$

$$ - \frac{2}{5} \cdot 5^x = -10 $$

$$ 5^x = 25 $$

$$ x = 2 $$

Ответ: 2