9^x+2 = 240 + 9^x , what is x?

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Solution

Given 9^x+2 = 240 + 9^x
⇒ 9^xx 9²= 240 + 9^x
let 9^x = a
⇒ 81a = 240 + a
⇒ 80a = 240
⇒ a = 3
but 9^x = a
⇒ 9^x = 3
⇒ 3^2x = 3
bases are equal powers should be equated.
⇒ 2x = 1
⇒ x = 1/2.

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