Logarithmic function help

• Mar 9th 2011, 02:36 AM
dervast
Logarithmic function help
Dear all it have been many years since I stopped reading maths.

Today I have tried to solve the following equation. K is the only unknown factor. So I tried to keep only K in the right part of the equation and put all the others to the left side. As I am not good in math notations in internet please accept my attached image

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It seems that I luck some knowledge how to solve that.

Best Regards
Alex
• Mar 9th 2011, 02:59 AM
HallsofIvy
Your equation has "K" both inside a transcendental function, log(K), and outside it. Such equations cannot, in general be solved in terms of elementary functions. You might be able to solve for K in terms of "Lambert's W function" which is defined as the inverse function to \$\displaystyle f(x)= xe^x\$.
• Mar 9th 2011, 03:12 AM
dervast
Quote:

Originally Posted by HallsofIvy
Your equation has "K" both inside a transcendental function, log(K), and outside it. Such equations cannot, in general be solved in terms of elementary functions. You might be able to solve for K in terms of "Lambert's W function" which is defined as the inverse function to \$\displaystyle f(x)= xe^x\$.

Thanks a lot :)
Could you please provide me moe information? What is that Lambert's W function and how can I try to solve it?

Regards
Alex