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- anonymous

does anyone know an algebraic way to solve ln(t)-t=ln(9.21), a better question is there an algebraic way, I think there has to be

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- anonymous

- katieb

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- TuringTest

I don't think there is a simple algebraic way to do this. There are perhaps more advanced techniques
oh satellite know I bet

- anonymous

\[\ln(t)-t<0\] so there is no solution

- TuringTest

no real solution...

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- TuringTest

http://www.wolframalpha.com/input/?i=+solve+ln%28t%29-t%3Dln%289.21%29

- anonymous

you are not going to find that using algebra, i am almost certain

- anonymous

any ideas how wolfram took it to imaginary plane

- anonymous

ln(t)−t=2.22.....

- TuringTest

yeah
can't proceed from there because of what sat pointed out

- anonymous

what's the technique then to solve it going to imaginary numbers?

- TuringTest

It depends on the situation
de moivre, complex analysis, etc...
sometimes you can get imaginary numbers with just the quadratic formula

- anonymous

you usually define
\[\log(z)\] in the complex plane as
\[\log(z)=\log(r)+i\theta\] but the function is not single values unless you specify
\[0\leq \theta <2\pi\] or some other interval of length
\[2\pi\] because the polar form of a complex number is not unique

- anonymous

thanks for the help

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