Determine dom ain ${log}_{4} {log}_{5} {log}_{3} (18 x - x^{2} - 77)$ .
The domain of x can be expressed as $(a, b)$ , where $b > a$ , then $b - a = ?$

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Solution

${log}_{5} {log}_{3} (18 x - x^{2} - 77) > 0$
$\Rightarrow {log}_{3} (18 x - x^{2} - 77) > 5^{\circ} = 1$
$\Rightarrow 18 x - x^{2} - 77 > 3^{1}$
$\Rightarrow x^{2} - 18 x + 80 < 0$
$\Rightarrow (x - 8) (x - 10) < 0$
$∴ x ϵ (8, 10)$

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