145 1) $$2^x + 2^{x-3} = 18$$; 2) $$3^x + 4\cdot3^{x+1} = 13$$; 3) $$2\cdot3^{x+1} - 6\cdot3^{x-1} - 3^x = 9$$; 4) $$5^{x+1} + 3\cdot5^{x-1} - 6\cdot5^x + 10 = 0$$.

$$2^x + 2^{x-3} = 18$$

$$2^x + 2^x \cdot 2^{-3} = 18$$

$$2^x + 2^x \cdot \frac{1}{8} = 18$$

$$2^x(1 + \frac{1}{8}) = 18$$

$$2^x \cdot \frac{9}{8} = 18$$

$$2^x = 18 \cdot \frac{8}{9}$$

$$2^x = 2 \cdot 8$$

$$2^x = 16$$

$$2^x = 2^4$$

$$x = 4$$

Ответ: $$x = 4$$

$$3^x + 4\cdot3^{x+1} = 13$$

$$3^x + 4\cdot3^x \cdot 3 = 13$$

$$3^x(1 + 4\cdot3) = 13$$

$$3^x(1 + 12) = 13$$

$$3^x \cdot 13 = 13$$

$$3^x = 1$$

$$3^x = 3^0$$

$$x = 0$$

Ответ: $$x = 0$$

$$2\cdot3^{x+1} - 6\cdot3^{x-1} - 3^x = 9$$

$$2\cdot3^x \cdot 3 - 6\cdot3^x \cdot \frac{1}{3} - 3^x = 9$$

$$3^x(2\cdot3 - 6\cdot\frac{1}{3} - 1) = 9$$

$$3^x(6 - 2 - 1) = 9$$

$$3^x \cdot 3 = 9$$

$$3^x = 3$$

$$3^x = 3^1$$

$$x = 1$$

Ответ: $$x = 1$$

$$5^{x+1} + 3\cdot5^{x-1} - 6\cdot5^x + 10 = 0$$

$$5^x\cdot5 + 3\cdot5^x\cdot\frac{1}{5} - 6\cdot5^x + 10 = 0$$

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

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

$$5^x(\frac{25+3-30}{5}) + 10 = 0$$

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

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

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

$$5^x = 25$$

$$5^x = 5^2$$

$$x = 2$$

Ответ: $$x = 2$$