The set of values of $x$ for which the inequality $(3^{x} - 1) (4^{x} - 16) (x - 5) < 0$ is

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Solution

Let the given expression be $E : (3^{x} - 1) (4^{x} - 16) (x - 5) < 0$

$3^{x} - 1 = 0 \Rightarrow x = 0$

$4^{x} - 16 = 0 \Rightarrow x = 2$

$x - 5 = 0 \Rightarrow x = 5$

Use wavy curve method

Sign scheme of $E$ is shown below.

From above figure, we have $E < 0$ for $x \in (- \infty, 0) \cup (2, 5)$

Hence the correct answer is A.

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