I'm new to logarithms and I am having trouble solving this equation
$$ \left( \log_3 x \right)^2 + \log_3 (x^2) + 1 = 0.$$
How would I solve this? A step-by-step response would be appreciated.
Also, I know how to solve it with assigning $\log_3 (x)$ as $x$ and solving $x^2 + x + 1 = 0$, and getting the answer from there. I am looking to see how I would do it with just logarithms and no quadratics.