Question

Prove this

Answer 1

I give up, I can't

Answer 2

Okay so take the right side,
log(mn)= log m + log n by property.
and log(m/n)=log m - log n
So we have on the right side,
(log m + log n)(log m + n)= (logm)^2 - (logn)^2 which is equal to Left side.

Answer 3

I'm sure this question should say:
\[ (log m)^2 - (\log n)^2 = \log(mn).\log(m/n) \]

Answer 4

@JamesJ: Me too..same thing.

Answer 5

There is no way I am aware of, which can make x equal to n lol..

Answer 6

well that's what i thought, but i wasn't sure as i'm not an expert but i guess i thought right... in any case though i still wouldn't be able to move on from the question... any help from what u figured out?

Answer 7

When you're asked to prove something and can't see what to do, use the only things you do know: definition or basic rules.

In this case you know some basic rules: e.g.,
log(mn) = log m + log n
and
log(m/n) = log m - log n

Once you do that, the result suddenly becomes very clear.

Answer 8

Okay, lol
\[(\log m)^{2} - (\log x)^{2}= (\log m)^{2} - (\log n)^{2}\]
Cancel (log m)^2 and negative signs, so
\[(\log x)^{2} = (\log n)^{2}\]

Answer 9

This is the way I see it..maybe not the best way but how else would you prove x=n?

Answer 10

For what it's worth, the equation of the question does indeed imply
\[ (\log x)^2 = (\log n)^2 \]
which in turn implies
\[ \log x = \pm \log n \]
and hence
\[ x = n \ \ or \ \ 1/n \]

Answer 11

True, i think that's the effective answer.