Solve: e^2x=3(e^x)+4

Alyce Wilkinson

Alyce Wilkinson

Answered question

2021-08-15

Solve:
e2x=3(ex)+4

Answer & Explanation

Szeteib

Szeteib

Skilled2021-08-16Added 102 answers

We have to solve e2x=3(ex)+4 Let u=ex
Then given equation come:
u2=3u+4u23u4=0
By using quadratic formula we get
u=(3)±3241(4)21=3±9+162=4,1
Therefore we get
ex=4andex=1
By taking logarithm in the above two equations we get
x=ln(4) and x=ln(1)=0
Notice that x=0 does not satisfy the given equation.
Hence the only solution of the given equation is x=ln(4)=2ln(2)

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