Question

solve e^ (2 x)-6 e ^(x) = 8 , for x, x>1

Answer 1

Let y= e^x

y^2 -6y -8 = 0

y=7.123 ,y=-1.123

e^x = 7.123
x= ln(7.123)

Answer 2

Ignore -1.123 since \[x >1\]

Answer 3

\[Let, e ^{x}=a ,so , e ^{2x} =a ^{2}\]
\[a ^{2}-6a=8\]
\[a=4, a=-2\]
\[e ^{x}=-2,4\]
\[e ^{x}=-2 , Not -Possible\
\[So, e ^{x}=4\]
\[x=2\ln 2\]

Answer 4

thanks much