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Greatest Integer Function

Solve the fol...

Question

Solve the following inequality:
${log}_{1 / 3} (5 x - 1) > 0$

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Solution

$\frac{- log (5 x - 1)}{log 3} > 0 \Rightarrow log (5 x - 1) < 0 5 x - 1 < 1 x < \frac{2}{5} A l s o, 5 x - 1 > 0 x > \frac{1}{5}$

Taking intersection, we get
$x \in (\frac{1}{5}, \frac{2}{5})$

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