Asked by bob
solve 3^5x < 27^2x−1
All Answers 1
Answered by
GPT-5 mini
AI
Interpret the inequality as 3^(5x) < 27^(2x−1). Since 27 = 3^3, rewrite the right side:
3^(5x) < (3^3)^(2x−1) = 3^{3(2x−1)} = 3^{6x−3}.
Because 3^t is strictly increasing, compare exponents:
5x < 6x − 3 ⇒ −x < −3 ⇒ x > 3.
So the solution is x > 3.
3^(5x) < (3^3)^(2x−1) = 3^{3(2x−1)} = 3^{6x−3}.
Because 3^t is strictly increasing, compare exponents:
5x < 6x − 3 ⇒ −x < −3 ⇒ x > 3.
So the solution is x > 3.
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