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tanchik213
@tanchik213
August 2021
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Решите неравенство:
[tex] 3log^{2} _{4} x-7log _{4} 16x+30[/tex]<0
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nKrynka
Решение
3log²₄ x - 7log₄ 16x + 30 < 0
3log²₄ x - 7log₄ 16 - 7log₄ x + 30 < 0
3log²₄ x - 7log₄ (4³) - 7log₄ x + 30 < 0
3log²₄ x - 2*7*log₄ (4) - 7log₄ x + 30 < 0
3log²₄ x - 14 - 7log₄ x + 30 < 0
3log²₄ x - 7log₄ x + 16 < 0
log₄ x = t
3t² - 7t + 16 < 0
D = 49 - 4*3*16 < 0, решений нет
2 votes
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Answers & Comments
3log²₄ x - 7log₄ 16x + 30 < 0
3log²₄ x - 7log₄ 16 - 7log₄ x + 30 < 0
3log²₄ x - 7log₄ (4³) - 7log₄ x + 30 < 0
3log²₄ x - 2*7*log₄ (4) - 7log₄ x + 30 < 0
3log²₄ x - 14 - 7log₄ x + 30 < 0
3log²₄ x - 7log₄ x + 16 < 0
log₄ x = t
3t² - 7t + 16 < 0
D = 49 - 4*3*16 < 0, решений нет