log-2-8x-log-3-27x-x-2-x-0-

Question Number 90434 by john santu last updated on 23/Apr/20

\frac{\log_{2} (8 x) . \log_{3} (27 x)}{x^{2} - ∣ x ∣} ⩽ 0

Commented by jagoll last updated on 28/Apr/20

h o w \frac{1}{8} < \frac{1}{27} ?

Commented by john santu last updated on 23/Apr/20

(1) x > 0

\Rightarrow \frac{(8 x - 1) (27 x - 1)}{x^{2} - x} ⩽ 0

\frac{(x - \frac{1}{8}) (x - \frac{1}{27})}{x (x - 1)} ⩽ 0

\Rightarrow 0 < x ⩽ \frac{1}{27} \lor \frac{1}{8} ⩽ x < 1

Commented by mahdi last updated on 24/Apr/20

\frac{1}{8} ⩽ x ⩽ \frac{1}{27} \cup 1 ⩽ x

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