Multiply everything by #e^x#:
#6=e^x+5e^-x#
#6color(blue)(*e^x)=e^xcolor(blue)(*e^x)+5e^-xcolor(blue)(*e^x)#
#6color(blue)(e^x)=e^(x+color(blue)x)+5e^(-x+color(blue)x)#
#6color(blue)(e^x)=e^(2x)+5e^(0)#
#6color(blue)(e^x)=e^(2x)+5*1#
#6color(blue)(e^x)=e^(2x)+5#
#0=e^(2x)-6color(blue)(e^x)+5#
#0=(color(blue)(e^x))^2-6color(blue)(e^x)+5#
Let #u=e^x#:
#0=u^2-6u+5#
#0=(u-5)(u-1)#
#u=1,5#
Put #e^x# back in for #u#:
#color(white){color(black)(
(e^x=1,qquade^x=5),
(color(blue)ln(color(black)(e^x))=color(blue)ln(color(black)1),qquadcolor(blue)ln(color(black)(e^x))=color(blue)ln(color(black)5)),
(x=0,qquadx=color(blue)ln(color(black)5))):}#
These are the solutions. Hope this helped!
