Solve the equation. e^{4x}+4e^{2x}-21=0

Jaya Legge

Jaya Legge

Answered question

2021-10-02

Solve the equation.
e4x+4e2x21=0

Answer & Explanation

wornoutwomanC

wornoutwomanC

Skilled2021-10-03Added 81 answers

Step 1
A quadratic equation of the form x2+ax+bx+ab can be factored as (x+a)(x+b). For a factored quadratic equation (x+a)(x+b)=0 the solution is x=−a,−b.
Try to write the given equation as a quadratic equation. And then factor and solve the quadratic equation.
Step 2
Given equation is e4x+4e2x21=0. Take e2x=z. So the given equation becomes z2+4z21=0. Factor this quadratic using 4=7−3 and 7(−3)=−21.
z2+4z21=0
z2+7z3z21=0
z(z+7)3(z+7)=0
(z3)(z+7)=0
z=3,7
e2x=3,7
e2x=3
lne2x=ln3
2x=ln3
x=ln32

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