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Particular Solution of a Differential Equation

Solve the fol...

Question

Solve the following inequality:
${log}_{8} (x^{2} - 4 x + 3) ⩽ 1$

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Solution

$(x^{2} - 4 x + 3) > 0 (x - 3) (x - 1) > 0 x \in (- \infty, 1) \cup (3, \infty)$
and
$x^{2} - 4 x + 3 \leq 8 x^{2} - 4 x - 5 \leq 0 (x - 5) (x + 1) \leq 0 x \in [- 1, 5]$
Taking intersection, we get
$x \in [- 1, 1) \cup (3, 5]$

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