SOLUTION: Can someone please help? Solve the equation. e^(x+3) = e^(x) + 9 x=?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Can someone please help? Solve the equation. e^(x+3) = e^(x) + 9 x=?      Log On


   

Question 220533: Can someone please help?
Solve the equation.
e^(x+3) = e^(x) + 9
x=?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember that x%5E%28y%2Bz%29=x%5Ey%2Ax%5Ez. So this means that e%5E%28x%2B3%29=e%5Ex%2Ae%5E3. If you let z=e%5Ex you can rewrite the equation into e%5E3z=z%2B9 and easily solve for 'z' (since it's now a linear equation). Once you have the solution in terms of 'z', use the equation z=e%5Ex to find the solution in terms of 'x'.

Note: 'e' is just the constant number 2.71828...