Question

Очень срочно ! 50 баллов !

Answer 1

1)

$( \frac{1}{3} )^{x } = 81 \\ (\frac{1}{3} ^{x} ) = ( \frac{1}{3} ) ^{ - 4} \\ x = - 4$

2)

$0.5 ^{x} = 0.125 \\ {0.5}^{x} = {0.5}^{3} \\ x = 3$

3)

${0.3}^{2 - x} = 0.09 \\ {0.3}^{2 - x} = 0.3 ^{2} \\ 2 - x = 2 \\ - x = 2 - 2 \\ - x = 0 \\ x = 0$

4)

${5}^{3x - 10} = 25 \\ {5}^{3x - 10} = {5}^{2} \\ 3x - 10 = 2\\ 3x = 10 + 2 \\ 3x = 12 \\ x = 4$

5)

$(\frac{2}{9}) ^{x + 3} = 20 \frac{1}{4} \\ ( \frac{2}{9}) ^{x + 3} = \frac{81}{4} \\ ( \frac{2}{9}) ^{x + 3} = (\frac{9}{2}) {}^{2 } \\ ( \frac{2}{9}) ^{x + 3} = (\frac{2}{9}) {}^{ - 2 } \\ x + 3 = - 2 \\ x = - 2 - 3 \\ x = - 5$

6)

${3}^{x} - {3}^{x + 3} = - 78 \\ {3}^{x} (1 - 3 {}^{3} ) = - 78 \\ 3x \times ( - 8) = - 78 \\ 3x = \frac { 78}{8} \\ 3x = 9.75 \\ x = 3.25$

7)

${2}^{ {x}^{ 2} - x - 1 } = 32 \\ {2}^{ {x}^{ 2} - x - 1 } = {2}^{5} \\{ {x}^{ 2} - x - 1 } = {5} \\ { {x}^{ 2} - x - 6 } = 0 \\ d = ( - 1) {}^{2} - 4 \times 1 \times ( - 6) = \sqrt{25} = 5 \\ x1 = \frac{1 + 5}{2} = 3 \\ x2 = \frac{1 - 5}{2} = - 2$