Question

Log0.5 (4-x)+log0.5 (x-1)=-1
Аомогите решить

Answer 1

$log_{0.5}(4 - x) + log_{0.5}(x - 1) = - 1$

$log_{0.5}((4 - x)(x - 1)) = -1$

$log_{0.5}( - {x}^{2} + 5x - 4 ) = -1$

$log_{0.5}( - {x}^{2} + 5x - 4 ) = log_{0.5}( {0.5}^{ - 1} )$

$- {x}^{2} + 5x - 4 = 2$

${x}^{2} - 5x + 6 = 0$

${x}^{2} - 2x - 3x + 6 = 0$

x(x - 2) - 3(x - 2) = 0

(x - 3)(x - 2) = 0

x1 = 2

x2 = 3

Ответ: x = 2; x = 3