Exponential and logarithmic properties

AI Thread Summary
The equation 1180 = 98t + 1080e^(-t/10) presents a challenge due to the variable t appearing both inside and outside an exponential function. There is no elementary function that can simplify this equation directly. The Lambert's W function is suggested as a potential solution, as it serves as the inverse of the function f(x) = x * e^x. Utilizing a variation of the Lambert's W function may help in solving for t. This approach is recommended for tackling such complex equations involving exponentials.
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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.
 
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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)= xex.
A variation of that will "solve" your equation.
 
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