Question

Найдите x. 20 баловвв

Answer 1

$log_{x}(25 \sqrt{5} ) = - \frac{5}{8}, \: x \in (0;1) \cup (1 ;+ \infty ) \\ log_{x}( {5}^{2} {5}^{ \frac{1}{2} } ) = - \frac{5}{8} \\ log_{x}( {5}^{2 + \frac{1}{2} } ) = - \frac{5}{8} \\ log_{x}( {5}^{2.5} ) = - \frac{5}{8} \\ {x}^{ - \frac{5}{8} } = {5}^{2.5} \\ (x {}^{ - \frac{5}{8} } ) {}^{ - \frac{8}{5} } = ( {5}^{2.5} ) {}^{ - \frac{8}{5} } \\ x = {5}^{ - \frac{25 \times 8}{10 \times 5} } \\ x = {5}^{ - 4} \\ x = \frac{1}{625}$

Answer 2

Нашёл x, ответ 5^(-4)