Question

9^x+2 =240+9^x what is the value of x

Answer 1

9^x9^2 = 240 + 9 ^x
9^x 9^2 - 9 ^x= 240

9x(81 - 1 ) = 240

⇒ 9x (80) = 240

⇒ 3² x = 3.

⇒2x = 1

∴ x = 1/2.

Answer 2

9^x+2 = 240 +9^x
9^x * 9² = 240 +9^x since a^m+n = a^m * a^n

let 9^x = a---(1)
then
a*81 = 240 + a
81a -a=240
80a=240
a=240/80
a= 3

substitute a=3 in (1)
9^x = 3
3^2x =3^1here 9 = 3^2
therefore
2x =1 here we used [ if a^m = a^n then m=n]
x= 1/2