How to solve #2e^x -1 = 21e^(-x)#?

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Answer 1 · 2017-12-07T10:14:46

See below.

#21e^(-x)=21/e^x#

#2e^x-21/e^x-1=0#

Let #y=e^x#

#2y-21/y-1=0#

#2y^2-y-21=0#

Factor:

#(2y-7)(y+3)=0=>y=7/2 and y=-3#

( -3 would give complex solution)

If #y=7/2#

#e^x=7/2#

#x=ln(7/2)#

If #y=-3#

#e^x=-3#

#x=ln(-3)#