What is the solution for log(3) x^2 + log(9) x = 2?

The equation to be solved is log(3) x^2 + log(9) x =
2

Use the following properties of
logarithms

log a^b = b*log a , log a + log b = log a*b and
log (b) c = log(a)c / log(a)b

log(3) x^2 + log(9) x =
2

=> log(3) x^2 + log(3) x / log(3) 9 =
2

=> log(3) x^2 + log(3) x / log(3) 3^2 =
2

=> log(3) x^2 + log(3) x^(1/2) =
2

=> log(3) x^2*x^(1/2) =
2

=> log(3) x^(5/2) =
2

=> x^(5/2) =
9

=> x =
9^(2/5)

=> x = 2.4082 (
approximately)

The solution of the equation
is x = 2.4082