## anonymous 4 years ago 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

1. 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

2. anonymous

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

3. TuringTest

no real solution...

4. TuringTest
5. anonymous

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

6. anonymous

any ideas how wolfram took it to imaginary plane

7. anonymous

ln(t)−t=2.22.....

8. TuringTest

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

9. anonymous

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

10. TuringTest

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

11. 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

12. anonymous

thanks for the help