If-9-x-4-3-x-2-3-5-0-then-the-solution-set-is-

Question Number 27258 by hasie09 last updated on 04/Jan/18

If 9^{x} - 4 \times 3^{x + 2} + 3^{5} = 0, then the solution

set is

Commented by tawa tawa last updated on 04/Jan/18

{(3^{2})}^{x} - (4 \times 3^{x} \times 3^{2}) + 243 = 0

{(3^{x})}^{2} - (4 \times 3^{x} \times 9) + 243 = 0

Let 3^{x} = y

∴ y^{2} - (4 \times y \times 9) + 243 = 0

∴ y^{2} - 36 y + 243 = 0

∴ y^{2} - 27 y - 9 y + 243 = 0

∴ (y^{2} - 27 y) - (9 y + 243) = 0

∴ y (y - 27) - 9 (y - 27) = 0

∴ (y - 27) (y - 9) = 0

∴ y - 27 = 0 or y - 9 = 0

∴ y = 27 or y = 9

Remember : 3^{x} = y

when y = 27

∴ 3^{x} = 27

∴ 3^{x} = 3^{3}

Since the base are equal

∴ x = 3

when y = 9

∴ 3^{x} = 9

∴ 3^{x} = 3^{2}

Since the base are equal

∴ x = 2

Therefore, x = 3 or x = 2