SOLUTION: Hi, could you please help me with this question: 3e^x = 5 + 8e^-x - How do you solve for x when the power is negative? Thanks!

1.  First step: introduce new variable u = .

    Then your equation takes the form

    3u = 5 + .    (1)



2.  Second step:  multiply by "u" both sides:

     3u^2 = 5u + 8,   or

     3u^2 - 5u - 8 = 0.



3.  You got quadratic equation. Its roots are

     =  = .


    a)   =  =  = ;

        ========>   =   ====>  x = .


    b)   =   = -1.

        ========>    = -1   ====> There is NO solution for x.


Answer.  The given equation has a unique solution  x = .