Question

Показательные уравнения

1) $2^{x-6x-2,5} =16\sqrt{2}$

2) $2^{3x-1} =(0,25)^{1-x} *8$

Answer 1

$1) {2}^{x - 6x - 2.5} = 16 \sqrt{2} \\ {2}^{ - 5x - 2.5} = {2}^{4} \times {2}^{ \frac{1}{2} } \\ {2}^{ - 5x - 2.5} = {2 }^{ \frac{9}{2} } \\ {2}^{ - 5x - 2.5} = {2}^{4.5} \\ - 5x - 2.5 = 4.5 \\ - 5x = 7 \\ x = - \frac{7}{5} = - 1.4$

$2) {2}^{(3x - 1)} = {0.25}^{(1 - x)} \times 8 \\ {2}^{(3x - 1)} = { (\frac{1}{4}) }^{(1 - x)} \times {2}^{3} \\ {2}^{(3x - 1)} = {( {2}^{ - 2}) }^{(1 - x)} \times {2}^{3} \\ {2}^{(3x - 1)} = {2}^{( - 2(1 - x) + 3)} \\ {2}^{(3x - 1)} = {2}^{(2x + 1)} \\ 3x - 1 = 2x + 1 \\ x = 2$