# Solve for x of an exponential function

1. Dec 2, 2008

### sara_87

1. The problem statement, all variables and given/known data

e^(2x+9) - 4e^x -5 = 0

2. Relevant equations

3. The attempt at a solution
I changed this into: e^(2x+9) =4e^x + 5
I took logarithm of both sides:
2x+9=ln(4e^x +5)

but i dont know what to do with the right hand side.
what will be the easiest way to solve this?
Thank you very much

2. Dec 2, 2008

### rochfor1

Try this,
\begin{align*} 0 & = e^{ 2 x + 9 } - 4 e^x - 5 \\ & = e^9 e^{ 2 x } - 4 e^x - 5. \end{align*}

Then the substitution $$u=e^x$$ turns this into a quadratic equation, which is easily solved, and then $$x = \ln u$$.

3. Dec 2, 2008

### sara_87

excellent.
thank you v much