Реши уравнения: 1) 3 ⋅ 9^x = 81; 2) 2 ⋅ 4^x = 64; 3) 3^{x+1/2} ⋅ 3^{x-2} = 1; 4) 0,5^{x+7} ⋅ 0,5^{1-2x} = 2; 5) 0,6^x ⋅ 0,6^3 = 0,6^{2x} / 0,6^5; 6) 6^{3x} ⋅ 1/6 = 6 ⋅ (1/6)^{2x}

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Реши уравнения: 1) 3 ⋅ 9^x = 81; 2) 2 ⋅ 4^x = 64; 3) 3^{x+1/2} ⋅ 3^{x-2} = 1; 4) 0,5^{x+7} ⋅ 0,5^{1-2x} = 2; 5) 0,6^x ⋅ 0,6^3 = 0,6^{2x} / 0,6^5; 6) 6^{3x} ⋅ 1/6 = 6 ⋅ (1/6)^{2x}

$Реши уравнения: 1) 3 ⋅ 9^x = 81; 2) 2 ⋅ 4^x = 64; 3) 3^{x+1/2} ⋅ 3^{x-2} = 1; 4) 0,5^{x+7} ⋅ 0,5^{1-2x} = 2; 5) 0,6^x ⋅ 0,6^3 = 0,6^{2x} / 0,6^5; 6) 6^{3x} ⋅ 1/6 = 6 ⋅ (1/6)^{2x}$

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1) $3 \cdot 9^x = 81$ $9^x = 27$ $(3^2)^x = 3^3$ $3^{2x} = 3^3$ $2x = 3$ $x = \frac{3}{2} = 1.5$ 2) $2 \cdot 4^x = 64$ $4^x = 32$ $(2^2)^x = 2^5$ $2^{2x} = 2^5$ $2x = 5$ $x = \frac{5}{2} = 2.5$ 3) $3^{x+\frac{1}{2}} \cdot 3^{x-2} = 1$ $3^{x+\frac{1}{2} + x - 2} = 1$ $3^{2x - \frac{3}{2}} = 3^0$ $2x - \frac{3}{2} = 0$ $2x = \frac{3}{2}$ $x = \frac{3}{4} = 0.75$ 4) $0.5^{x+7} \cdot 0.5^{1-2x} = 2$ $0.5^{x+7+1-2x} = 2$ $0.5^{8-x} = 2$ $(2^{-1})^{8-x} = 2^1$ $2^{x-8} = 2^1$ $x-8 = 1$ $x = 9$ 5) $0.6^x \cdot 0.6^3 = \frac{0.6^{2x}}{0.6^5}$ $0.6^{x+3} = 0.6^{2x-5}$ $x+3 = 2x-5$ $x = 8$ 6) $6^{3x} \cdot \frac{1}{6} = 6 \cdot (\frac{1}{6})^{2x}$ $6^{3x-1} = 6 \cdot 6^{-2x}$ $6^{3x-1} = 6^{1-2x}$ $3x-1 = 1-2x$ $5x = 2$ $x = \frac{2}{5} = 0.4$ **Ответы:** 1) $x = 1.5$ 2) $x = 2.5$ 3) $x = 0.75$ 4) $x = 9$ 5) $x = 8$ 6) $x = 0.4$

Реши уравнения: 1) 3 ⋅ 9^x = 81; 2) 2 ⋅ 4^x = 64; 3) 3^{x+1/2} ⋅ 3^{x-2} = 1; 4) 0,5^{x+7} ⋅ 0,5^{1-2x} = 2; 5) 0,6^x ⋅ 0,6^3 = 0,6^{2x} / 0,6^5; 6) 6^{3x} ⋅ 1/6 = 6 ⋅ (1/6)^{2x}

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