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Question Number 40544 by mondodotto@gmail.com last updated on 23/Jul/18

$$\mathbf{solve}\mathbf{for}\mathit{x}$$$$3^{(2\mathit{x}-1)}-4\left(3^{\mathit{x}}\right)+1=0$$

Answered by tanmay.chaudhury50@gmail.com last updated on 23/Jul/18

$$3^{2x}.3^{-1}-4.3^x+1=0$$$$a=3^x$$$$a^2\times \frac{1}{3}-4a+1=0$$$$a^2-12a+3=0$$$$a=\frac{12\pm \sqrt{144-12}}{2}=\frac{12\pm \sqrt{132}}{2}$$$$a=\frac{12\pm 2\sqrt{33}}{2}=6\pm \sqrt{33}$$$$3^x=6\pm \sqrt{33}$$$$x={log}_3(6\pm \sqrt{33})$$

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