Solve for t: `xe^(2t) + x =e^(2t) - 1`  

1 Answer | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The equation `xe^(2t) + x =e^(2t) - 1` has to be solved for t.

`xe^(2t) + x =e^(2t) - 1`

=> `x*e^(2t) - e^(2t) = -x - 1`

=> `e^(2t)(x - 1) = (-x - 1)`

=> `e^(2t) = (1 + x)/(1 - x)`

take the natural logarithm of both the sides

`ln e^(2t) = ln((1 + x)/(1 - x))`

=> `2t*ln e = ln((1 + x)/(1 - x))`

=> `2t = ln((1 + x)/(1 - x))`

=> `t = ln((1 + x)/(1 - x))/2`

The solution for t is `t = ln((1 + x)/(1 - x))/2`

We’ve answered 318,945 questions. We can answer yours, too.

Ask a question