To solve this logarithmic equation, we will first use the properties of logarithms to simplify it.

Recall the following properties of logarithms:

log(a) + log(b) = log(a*b)log(a) - log(b) = log(a/b)log(a^n) = n*log(a)

Applying these properties to the given equation, we have:

9log(x) - log(x) - log(5) + 2 = 0
8log(x) - log(5) + 2 = 0
log(x^8) - log(5) + 2 = 0
log(x^8/5) + 2 = 0
log(x^8/5) = -2

Now, we can rewrite the equation in exponential form:

x^8/5 = 10^(-2)
x^8/5 = 1/100
x^8 = 5/100
x^8 = 1/20

Taking the eighth root of both sides to solve for x, we get:

x = (1/20)^(1/8)
x = 1/√(20)
x = 1/√(4*5)
x = 1/(2√5)

Therefore, the solution to the equation log125(x^9) - log(x)5 + 2 = 0 is x = 1/(2√5)