Question 1042616
e^4x+5e^2x-24=0 
Treat it as a quadratic with e^2x=x
x^2+5x-24=0
(x+8)(x-3)=0
(e^2x+8)(e^2x-3)=0
e^2x=-8; ln of both sides means ln -8, and that doesn't exist, so ignore that root.
e^2x=3, setting the factor equal to 0 and adding 3 to both sides
Take the ln of both sides.  ln e^2x=2x, since ln and e cancel each other out.
2x=ln 3
x=(1/2)ln 3, exact answer.  The numerical answer is 0.5493


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e^2ln3+5e^ln3-24;
but e^2ln3=e^ln(9) by property of logs
e^ln9+5 e^ln3-24=9+15-24=0.