Помогите решить уравнение (номер 845)

Решите задачу:

$7 {x}^{ \frac{1}{ { log_{2}^{2}( {x}^{3} ) } } + log_{x}(2)} = 5 + {(x + 7)}^{ \frac{2}{ log_{ \sqrt{2} }(x + 7)} } \\ 7 {x}^{ \frac{1}{ { 9log_{2}^{2}( {x } )} } + log_{x}(2)} = 5 + {(x +7)}^{2 log_{(x + 7)}( \sqrt{2} ) } \\ 7 {x}^{ \frac{1}{9} log_{x}^{2}(2) + log_{x}(2) } = 5 + 2 = 7\\ {x}^{ \frac{1}{9} log_{x}^{2}(2) + log_{x}(2) } = 1 \\ log_{2}({x}^{ \frac{1}{9} log_{x}^{2}(2) + log_{x}(2) }) = log_{2}(1) \\ (\frac{1}{9} log_{x}^{2}(2) + log_{x}(2)) log_{2}(x) = 0 \\ \frac{1}{9} log_{x}(2) + 1 = 0 \\ log_{x}(2) = - 9 \\ {x}^{ - 9} = 2 \\ x = {2}^{ - \frac{1}{9} }$