Question

if 9 to the power x+ 2 is equal to 240 + 9 to the power x find x

Answer 1

Answer :



Now, 9ˣ⁺² = 240 + 9ˣ

⇒ 9ˣ × 9² = 240 + 9ˣ

⇒ 81 × 9ˣ = 240 + 9ˣ

⇒ (81 - 1) × 9ˣ = 240

⇒ 80 × 9ˣ = 240

⇒ 9ˣ = 240/80

⇒ 9ˣ = 3

⇒ (3²)ˣ = 3

⇒ 3²ˣ = 3¹

Now, comparing like powers of 3, we get

2x = 1

⇒ x = 1/2

∴ The required solution be x = 1/2

[Hope it helps you!]