What is the answer to e^{2x+2}+4(e^{x+2}-1)=e^x ?

The answer to e^{2x+2}+4(e^{x+2}-1)=e^x is x=-2

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e^{2x+2}+4(e^{x+2}-1)=e^x

e^{2 x + 2} + 4 (e^{x + 2} - 1) = e^{x}

x = - 2

Solution steps

e^{2 x + 2} + 4 (e^{x + 2} - 1) = e^{x}

Apply exponent rules

(e^{x})^{2} e^{2} + 4 (e^{x} e^{2} - 1) = e^{x}

Rewrite the equation with

e^{x} = u

(u)^{2} e^{2} + 4 (u e^{2} - 1) = u

Solve

u^{2} e^{2} + 4 (u e^{2} - 1) = u : u = \frac{- 4 e ^{2} + 1 + 16 e ^{4} + 8 e ^{2} + 1}{2 e ^{2}}, u = \frac{- 4 e ^{2} + 1 - 16 e ^{4} + 8 e ^{2} + 1}{2 e ^{2}}

u = \frac{- 4 e ^{2} + 1 + 16 e ^{4} + 8 e ^{2} + 1}{2 e ^{2}}, u = \frac{- 4 e ^{2} + 1 - 16 e ^{4} + 8 e ^{2} + 1}{2 e ^{2}}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = \frac{- 4 e ^{2} + 1 + 16 e ^{4} + 8 e ^{2} + 1}{2 e ^{2}} : x = - 2

Solve

e^{x} = \frac{- 4 e ^{2} + 1 - 16 e ^{4} + 8 e ^{2} + 1}{2 e ^{2}} :

No Solution for

x \in R

x = - 2

3600 = (0.78)^{x} 14500

3^{x} - 6^{3 x + 1} = 0

1200000 = 600000 e^{0.05 t}

9^{x} = 2 7^{x - 2}

e^{2 x} = e^{7 x}

What is the answer to e^{2x+2}+4(e^{x+2}-1)=e^x ?
The answer to e^{2x+2}+4(e^{x+2}-1)=e^x is x=-2