Question

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

Answer 1

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

oh satellite know I bet

Answer 2

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

Answer 3

no real solution...

Answer 4

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

Answer 5

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

Answer 6

any ideas how wolfram took it to imaginary plane

Answer 7

ln(t)−t=2.22.....

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

thanks for the help