Answer
$x=1.946$
$x=1.792$
Work Step by Step
$e^{2x}-13e^x+42=0$
$(e^x)^2-13(e^x)+42=0~~$ ($a=1,b=-13,c=42$):
$e^x=\frac{-b±\sqrt {b^2-4ac}}{2a}=\frac{-(-13)±\sqrt {(-13)^2-4(1)(42)}}{2(1)}=\frac{13±\sqrt {1}}{2}=\frac{13±1}{2}$
$e^x=7$
$\ln e^x=\ln7$
$x=\ln7=1.946$
$e^x=6$
$\ln e^x=\ln6$
$x=\ln6=1.792$
