solve-for-x-3-2x-1-4-3-x-1-0-

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

solve for x

3^{(2 x - 1)} - 4 (3^{x}) + 1 = 0

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

3^{2 x} . 3^{- 1} - 4 . 3^{x} + 1 = 0

a = 3^{x}

a^{2} \times \frac{1}{3} - 4 a + 1 = 0

a^{2} - 12 a + 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 = {l o g}_{3} (6 \pm \sqrt{33})