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Question Number 77183 by jagoll last updated on 04/Jan/20
what is x satisfy inequality 3^x^2 × 5^(x−1) ≥ 3
whatisxsatisfyinequality3x2×5x−1⩾3
Answered by john santu last updated on 04/Jan/20
⇒ 3^x^2 × 3^(log_3 (5^(x−1) )) ≥ 3 3^(x^2 +log_3 (5^(x−1) )) ≥ 3 x^2 +log_3 (5^(x−1) )−1≥0 (x−1)(x+1)+(x−1)log_3 (5) ≥ 0 (x−1){x+log_3 (15)}≥0 ⇒ x≥ 1 ∨ x ≤ −log_3 (15)
⇒3x2×3log3(5x−1)⩾33x2+log3(5x−1)⩾3x2+log3(5x−1)−1⩾0(x−1)(x+1)+(x−1)log3(5)⩾0(x−1){x+log3(15)}⩾0⇒x⩾1∨x⩽−log3(15)
Commented by jagoll last updated on 04/Jan/20
thanks sir
thankssir

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