To solve this logarithmic equation, we will first use the property of logarithms that states:

log_a(b) = log_a(c) if and only if b = c

Therefore, we can rewrite the equation as:

x^2 + x = x^2 + 3

Subtracting x^2 from both sides of the equation, we get:

x = 3

Therefore, the solution to the equation log3(x^2+x)=log3(x^2+3) is x = 3.