MHB How to Simplify this Complex Logarithm Expression?

Elena1
Messages
24
Reaction score
0
1) $( \log_{a}\left({b}\right)+\log_{b}\left({a}\right)+2) (\log_{a}\left({b}\right)-\log_{ab}\left({b)}\right)* \log_{b}\left({a}\right)-1=$?
 
Mathematics news on Phys.org
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:

MHB Rules said:
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.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

Similar threads

Replies
2
Views
2K
Replies
11
Views
4K
Replies
2
Views
2K
Replies
2
Views
2K
Replies
5
Views
1K
Back
Top