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log-9x-1-3-x-3-3-log-3x-2-1-3-27x-3-




Question Number 92980 by john santu last updated on 10/May/20
log _((9x))^(1/(3  ))   ((√(x^3 /3))) + log _((3x^2 ))^(1/(3  ))  ((√(27x))) ≤ 3
$$\mathrm{log}\:_{\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}{x}}} \:\left(\sqrt{\frac{{x}^{\mathrm{3}} }{\mathrm{3}}}\right)\:+\:\mathrm{log}\:_{\sqrt[{\mathrm{3}\:\:}]{\mathrm{3}{x}^{\mathrm{2}} }} \left(\sqrt{\mathrm{27}{x}}\right)\:\leqslant\:\mathrm{3} \\ $$
Answered by frc2crc last updated on 10/May/20
(1/9)<x<((√3)/3) or 3^(1/3) ≤x≤3
$$\frac{\mathrm{1}}{\mathrm{9}}<{x}<\frac{\sqrt{\mathrm{3}}}{\mathrm{3}}\:{or}\:\mathrm{3}^{\mathrm{1}/\mathrm{3}} \leqslant{x}\leqslant\mathrm{3} \\ $$
Commented by john santu last updated on 10/May/20
good
$$\mathrm{good}\: \\ $$

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