Solve for x of an exponential function

[sara_87]

Homework Statement

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

Homework Equations

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 don't know what to do with the right hand side.
what will be the easiest way to solve this?
Thank you very much

 

[rochfor1]

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

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

 

[sara_87]

excellent.
thank you v much