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Question Number 77183 by jagoll last updated on 04/Jan/20

$$\mathrm{what}\mathrm{is}\mathrm{x}$$$$\mathrm{satisfy}\mathrm{inequality}$$$$3^{{\mathrm{x}}^2}\times 5^{\mathrm{x}-1}⩾3$$

Answered by john santu last updated on 04/Jan/20

$$\Rightarrow 3^{x^2}\times 3^{{\log }_3\left(5^{x-1}\right)}⩾3$$$$3^{x^2+{\log }_3\left(5^{x-1}\right)}⩾3$$$$x^2+{\log }_3\left(5^{x-1}\right)-1⩾0$$$$(x-1)(x+1)+(x-1){\log }_3\left(5\right)⩾0$$$$(x-1)\{x+{\log }_3\left(15\right)\}⩾0$$$$\Rightarrow x⩾1\vee x⩽-{\log }_3\left(15\right)$$

Commented by jagoll last updated on 04/Jan/20

$$\mathrm{thanks}\mathrm{sir}$$

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