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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Show some effort. If you want help with a question we expect you to show some effort. Effort might include showing your work, learning how to typeset equations using $\LaTeX$, making your question clearer, titling threads effectively and posting in the appropriate subforum, making a genuine attempt to understand the given help before asking for more help, and learning from previously asked questions. Moderators reserve the right to close threads in cases where the member is not making a genuine effort (particularly if the member is flooding the forums with multiple questions of the same type). You also should remember that all contributors to MHB are unpaid volunteers and are under no obligation to answer a question.
 
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