Question

решить уравнение log2(x-3)=log0.5x

Answer 1

$log_{2}(x - 3) = - log_{2}(x) \\ log_{2}(x - 3) = log_{2}( \frac{1}{x} ) \\ x - 3 = \frac{1}{x} \\ {x }^{2} - 3x = 1 \\ {x}^{2} - 3x - 1 = 0 \\ d = 9 + 4 = 13 \\ x1 = \frac{3 - \sqrt{13} }{2} \\ x2 = \frac{3 + \sqrt{13} }{2}$

Answer 2

log(2)(x-3)=log(0,5)x
x-3>0;x>0;x>3 это ОДЗ
log(2)(x-3)=-log(2)x
log(2)(x-3)=log(2)x^(-1)
x-3=1/x
(x²-3x-1)/x=0;x≠0
x²-3x-1=0
D=9+4=13
x=(3±√13)/2
ответ (3+√13)/2