1. Exponential Equation in Quadratic Form

I am curious as to how i am to solve and equation with a negative exponent.
My problem is:
10e^x-15-45e^-x=0
We are suppose to use the formula that u=e^x.
I don't know what to do since there is a negative after the 45.

2. Re: Exponential Equation in Quadratic Form

Originally Posted by paigesisco
10e^x-15-45e^-x=0
We are suppose to use the formula that u=e^x.
I don't know what to do since there is a negative after the 45.
$\displaystyle \\10e^x-15-45e^{-x}=0\\10e^{2x}-15e^x-45=0\\2e^{2x}-3e^x-9=0\\(2e^x+3)(e^x-3)=0$

3. Re: Exponential Equation in Quadratic Form

Can you explain the method you used so that i can use it on future problems? I am confused on how the x's transfered

4. Re: Exponential Equation in Quadratic Form

Originally Posted by paigesisco
Can you explain the method you used so that i can use it on future problems? I am confused on how the x's transfered
Take the original equation an multiply all terms by $\displaystyle e^x$.