Exponential and logarithmic properties

[fisico]

Hi. I'm having trouble solving for t:

1180 = 98t + 1080e^(-t/10)

I know basic properties but I think I am not remembering some idea or specific property to be able to solve this. Thank you for any help.

 

[HallsofIvy]

Since the variable, t, appears both "inside" an exponential and "outside" there is no elementary function that will reduce that equation. You might look at "Lambert's W function" (check
http://en.wikipedia.org/wiki/Lambert's_W_function) which is defined[\b] as the inverse of the function f(x)= xe^x.
A variation of that will "solve" your equation.