What is the answer to e^{x^2}-e^5e^{x-1}=0 ?

The answer to e^{x^2}-e^5e^{x-1}=0 is x=(1+sqrt(17))/2 ,x=(1-sqrt(17))/2

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e^{x^2}-e^5e^{x-1}=0

e^{x^{2}} - e^{5} e^{x - 1} = 0

x = \frac{1 + 17}{2}, x = \frac{1 - 17}{2}

Decimal Notation

x = 2.56155 \dots, x = - 1.56155 \dots

Solution steps

e^{x^{2}} - e^{5} e^{x - 1} = 0

Add

e^{5} e^{x - 1}

to both sides

e^{x^{2}} - e^{5} e^{x - 1} + e^{5} e^{x - 1} = 0 + e^{5} e^{x - 1}

Simplify

e^{x^{2}} = e^{5} e^{x - 1}

Apply exponent rules

x^{2} = x + 4

Solve

x^{2} = x + 4 : x = \frac{1 + 17}{2}, x = \frac{1 - 17}{2}

x = \frac{1 + 17}{2}, x = \frac{1 - 17}{2}

11 (3 + e^{- x})^{- 1} = 2

11 (3 + e^{- x})^{- 1} = 3

8^{(x + 3)} = 32

2^{x - 1} = 256

62 = 75 e^{- 10 k}

What is the answer to e^{x^2}-e^5e^{x-1}=0 ?
The answer to e^{x^2}-e^5e^{x-1}=0 is x=(1+sqrt(17))/2 ,x=(1-sqrt(17))/2