Question

СРОЧНО логарифмическое уравнение​

Answer 1

ОДЗ :

1) x > 0

2) x ≠ 1

$log_{x}5\sqrt{5}-1,25=log_{x}^{2}\sqrt{5} \\\\log_{x}^{2} 5^{\frac{1}{2}}-log_{x}5^{\frac{3}{2}}+1,25=0\\\\\frac{1}{4}log_{x}^{2}5-\frac{3}{2}log_{x}5+1,25=0|*4\\\\log_{x}^{2}5-6log_{x} 5+5=0\\\\1)log_{x}5=1\\\\x_{1} =5\\\\2)log_{x}5=5\\\\x^{5}=5\\\\x_{2}=\sqrt[5]{5}\\\\Otvet:\boxed{5;\sqrt[5]{5}}$