Question

Показательные уравнения

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

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

Answer 1

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

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