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Quadratic Formula

Solve: log2...

Question

Solve: ${log}_{2} (\frac{x - 4}{2 x + 5}) < 1$ .

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Solution

A] $l o g_{2} ((x - 4) / (2 x + 5)) < 1$
$= (x - 4) / (2 x + 5) < 2$
$= x - 4 < 4 x + 10$
$= 0 < 4 x - x + 10 + 4$
$= 0 < 3 x + 14$
$∴$ $x > \frac{- 14}{3}$

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