MHB How to Simplify this Complex Logarithm Expression?

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The discussion revolves around simplifying the complex logarithmic expression $$$ ( \log_{a}(b) + \log_{b}(a) + 2) (\log_{a}(b) - \log_{ab}(b)) \log_{b}(a) - 1 $$$. Participants emphasize the importance of showing prior efforts and understanding of the problem to receive effective help. The forum encourages users to clarify their questions and provide context to facilitate better responses. Additionally, adherence to community guidelines is stressed, particularly regarding the demonstration of effort in problem-solving. Overall, the thread highlights the collaborative nature of the forum and the expectation for users to engage meaningfully.
Elena1
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1) $( \log_{a}\left({b}\right)+\log_{b}\left({a}\right)+2) (\log_{a}\left({b}\right)-\log_{ab}\left({b)}\right)* \log_{b}\left({a}\right)-1=$?
 
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Elena said:
1) ( \log_{a}\left({b}\right)+\log_{b}\left({a}\right)+2) (\log_{a}\left({b}\right)-\log_{ab}\left({b)}\right)* \log_{b}\left({a}\right)-1=?

You need to enclose your $\LaTeX$ code within tags, such as $$$$.

We also expect for people posting questions to show what they have tried, where they are stuck, so we can offer better, more specific help. This is outlined in MHB rule #11:

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