Решите неравенство
[tex]{8}^{ log^{2} _{8}(x) } + {x}^{ log_{8}(x) } > 2 \times \sqrt[3]{2} [/tex]
[tex]{8}^{ log^{2} _{8}(x) } + {x}^{ log_{8}(x) } > 2 \times \sqrt[3]{2} [/tex]
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Ответ:
Объяснение:
(8^(log₈x))^log₈x +x^(log₈x)>2∛2
ОДЗ х>0
x^(log₈x)+x^(log₈x)>2∛2
2x^(log₈x)>2*∛2
x^(log₈x)>∛2
log₈x^(log₈x)>log₈∛2
(log₈x)log₈x>(1/9)log₂2
(log₈x)²>(1/3)²
log₈x>1/3 ; x>∛8 ; x>2
2) log₈x<-1/3 ; x<1/∛8 ; x<1/2
x∈(0;0,5)U(2;+∞)