Answer
$x=1.386$
or
$x=0.693$
Work Step by Step
Notice that $e^{2x}=(e^x)^2$.
First we solve the equation for $e^x$:
$e^{2x}-6e^x+8=0$
$(e^x)^2-6(e^x)+8=0~~$ ($a=1,~b=-6,~c=8$)
$e^x=\frac{-(-6)±\sqrt {(-6)^2-4(1)(8)}}{2(1)}=\frac{6±\sqrt 4}{2}=\frac{6±2}{2}=3±1$
First solution:
$e^x=4$
$\ln e^x=\ln4~~$ (Using the Inverse Property $\ln e^x=x$):
$x=\ln4=1.386$
Second solution:
$e^x=2$
$\ln e^x=\ln2~~$ (Using the Inverse Property $\ln e^x=x$):
$x=\ln2=0.693$
