How do you solve the exponential inequality $2^{4 x} \geq 8^{x + 5}$ $2^(4x)>=8^(x+5)$ ?

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Answer 1 · 2017-08-12T12:37:35

Solution : $x \geq 15 or [15, \infty)$ $x >= 15 or [15,oo)$

$2^{4 x} \geq 8^{x + 5} or 2^{4 x} \geq 2^{3 (x + 5)}$ $2^(4x) >= 8^(x+5) or 2^(4x) >= 2^(3(x+5))$ or

$4 x \geq 3 (x + 5) or 4 x \geq 3 x + 15 or (4 x - 3 x) \geq 15$ $4x >= 3(x+5) or 4x >= 3x +15 or (4x-3x) >= 15$ or

$x \geq 15$ $x >= 15$

Solution : $x \geq 15 or [15, \infty)$ $x >= 15 or [15,oo)$ {Ans]

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