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Find the set of all real values of x that satisfy the inequality |9^x − 3^(x+1) − 15| < 2·9^x − 3^x.

1. (−∞, 1]
2. (1, ∞)
3. (−∞, 1]
4. None of these

Correct answer: (1, ∞)

Solution

Let t=3^x>0. RHS 2t^2-t must be positive (t>1/2). For 1/2<t<5.65 the inside is negative, so |t^2-3t-15|=15+3t-t^2; the inequality becomes 3t^2-4t-15>0 -> t>3 -> 3^x>3 -> x>1. Hence (1, infinity).

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