Solve for x: 9^x-3^x-8=0

Answer 1

(3^2)^x-3^x-8=0,
(3^x)² -3^x -8 = 0,
3^x =y,
y² -y - 8=0,
y= (1±√33)/2.
Since 3^x>0, the negative root is nonsence,
=> y= (1+√33)/2 =3.37228,
3^x =3.37228,
x=log(3)3.37228= =ln3.37228/ln3≈1.21559/1.0986=1.1065

Test:
9^1.1065 – 3^1.1065 – 8 =
=11.372 – 3.372 – 8 = 0