# Simplification of a logarithm expression

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:

$\log_2(x^2)/\log_2(9)$

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:

$\log_b(x) = \log_c(x) /\log_c(b)$

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

Can someone help me with this? Thank you.

• Unless you know $x$ you cannot evaluate $\log_2 x^2$ to a particular number. If the answer is $3$, then you must have $x=c^{3 \log_c 3}$, for whatever base $c$ you use. – copper.hat Mar 18 '15 at 16:59
• ...or unless you were given an equality for that expression. – Timbuc Mar 18 '15 at 17:03
• Is it possible you already know $x=27$? Could you give more context for your problem? – Peter Woolfitt Mar 18 '15 at 17:07
• I'm afraid the 'Simplify' the original expression is the only information I have. We haven't been given a known value for $x$. There is no inequality either. – bugdrown Mar 18 '15 at 17:16
• User201569, below, suggests that $log_3|x|$ would be the simplified form. Do others concur? – bugdrown Mar 18 '15 at 17:23

• I don't know. So you're saying we could take the square root of the base and use the absolute value of $x$? So $log_3|x|$ would be the simplified form? – bugdrown Mar 18 '15 at 17:20