SOLUTION: 11. Solve the exponential equation. Express your solutions in exact form only. Please show all of your work. e^x+15-e^x=4

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 11. Solve the exponential equation. Express your solutions in exact form only. Please show all of your work. e^x+15-e^x=4       Log On


   

Question 470759: 11. Solve the exponential equation. Express your solutions in exact form only. Please show all of your work.
e^x+15-e^x=4


Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
e%5E%28x+%2B+15%29+-+e%5Ex+=+4
Use property of exponent addition: x%5E2%2Ax%5E3+=+x%5E%282%2B3%29
e%5Ex%2Ae%5E15+-+e%5Ex+=+4
Factor out e^x
%28e%5Ex%29%28e%5E15+-+1%29+=+4
Divide by e^15 - 1 on both sides
e%5Ex+=+4%2F%28e%5E15+-+1%29
Take Natural Log of both sides
x+=+ln+%284%2F%28e%5E15+-+1%29%29+=+-13.61