Question

How do i solve e(to the 2x) - 6e (to the x) - 16 = 0

Answer 1

Tke e^x=m..then e^2x=(e^x)^2=m^2...so u have a quadratic eqn..m^2-6m-16=0..solve it...it'll give m=8,-2...so e^x=8..implies ln e^x=ln 8...so x=ln 8..since x ln e=x...similarly a second value is ln(-2) which is never possible...so ans is ln 8...

Answer 2

\(\large \begin{matrix}
e^{2x} &- 6e^x& - 16 = 0\\
1x^2&-6x&-16=0


\end{matrix}\)

thus is a quadratic equation, thus solve it likewise