Решить уравнение log8X+log√2 X = 14 смотреть приложение

log8 X + log √2 X = 14 ; log(2 ^ 3) X + log( 2 ^ 1 / 2 ) X = 14 ; 1 / 3 * log2 X + ( 1 / ( 1 / 2 ))log2 X = 14 ; 1 / 3 * log2 X + ( 1 * ( 2 / 1))log2 X = 14 ; 1 / 3 * log2 X + 2 * log2 X = 14 ; log2 X ^ ( 1 / 3 ) + 2 * log2 X = 14 ; log2 X ^ ( 1 / 3 ) + log2 X ^ 2= 14 ; log2 ( X ^ ( 1 / 3 ) * X ^ 2 ) = 14 ; ( X ^ ( 1 / 3 ) * X ^ 2 ) = 2 ^ 14 ; x ^ ( 1 / 3 + 2 ) = 2 ^ 14 ; x ^ ( ( 1 + 6) / 6 ) = 2 ^ 14 ; x ^ ( 7 / 6) = 2 ^ 14 ;( x ^ ( 7 / 6) ) ^ ( 1 / 7 ) = ( 2 ^ 14 ) ^ ( 1 / 7) ;x ^ ( 1 / 6 ) = 2 ^ 2 ;( x ^ ( 1 / 6 ) ) ^ 6= ( 2 ^ 2 ) ^ 6 ; x = 2 ^ 12 ; x = 4096 ;Ответ: 4 096 .