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PostPosted: Wed, 29 Feb 2012 15:13:22 UTC 
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what is the value of log x
and how can the below given exponential equation solved?

x^x=25


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PostPosted: Wed, 29 Feb 2012 15:18:49 UTC 
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Nayan wrote:
what is the value of log x
and how can the below given exponential equation solved?

x^x=25


You're not going to end up solving something like that. You can log both sides to get that x\log x=2\log 5 but that's about it.

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PostPosted: Wed, 29 Feb 2012 15:52:16 UTC 
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Shadow wrote:
Nayan wrote:
what is the value of log x
and how can the below given exponential equation solved?

x^x=25


You're not going to end up solving something like that. You can log both sides to get that x\log x=2\log 5 but that's about it.


... unless the OP knows about the Lambert W, which I don't expect.

Maybe the OP wants a numerical method ...

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\begin{aligned}
Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\
Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\
Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\
Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\
Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\
Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4
\end{aligned}


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