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Method of Intervals

Solve for x:3...

Question

Solve for $x$ :

$3 (9^{x}) < 8 (3^{x}) + 3$

A

(0,81)

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B

$(- \infty, 1)$

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C

$(- \infty, - 2) \cup (- 2, - 1) \cup (- 1, 0)$

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D

None of these.

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Solution

The correct option is B
$(- \infty, 1)$

Put $3^{x} = t$ to obtain
$3 t^{2} - 8 t - 3 < 0 \Rightarrow (3 t + 1) (t - 3) < 0 A s 3 t + 1 > 0, w e g e t t < 3 o r x < 1$

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