What is the answer to e^{2z}+e^z+1=0 ?

The answer to e^{2z}+e^z+1=0 is No Solution for z\in\mathbb{R}

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e^{2z}+e^z+1=0

e^{2 z} + e^{z} + 1 = 0

No Solution for z \in R

Solution steps

e^{2 z} + e^{z} + 1 = 0

Apply exponent rules

(e^{z})^{2} + e^{z} + 1 = 0

Rewrite the equation with

e^{z} = u

(u)^{2} + u + 1 = 0

Solve

u^{2} + u + 1 = 0 :

No Solution for

u \in R

No Solution for z \in R

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

2^{11 x} = 2^{x - 4}

4^{3 x + 1} = 1 6^{x + 3}

(2^{x}) (4^{x + 1}) = 8

7^{x + 3} = 4 9^{x + 3}

What is the answer to e^{2z}+e^z+1=0 ?
The answer to e^{2z}+e^z+1=0 is No Solution for z\in\mathbb{R}