How to simplify this logarithm expression: $\log_b(x) = \frac{\log_c(x) }{\log_c(b)}$?

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I need to verify the answer of a logarithm expression (note, I'm not a student). I managed to get through high school and college without ever having a math course that taught logarithms--I don't know how.

The expression that I need to simplify is:

$$\frac{\log_2(x^2)}{\log_2(9)}$$

The answer that was given was 3 but I have not been able to establish that this is correct despite finding plenty of information about logarithm rules and properties. It seems like the following property is applicable:

$$\log_b(x) = \frac{\log_c(x) }{\log_c(b)}$$

but I can only see that I would get me to $\log_9(x^2)$.

Can someone help me with this? Thank you.

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your answer is correct but isnot the most easiest form log9(x2)=log3|x|