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

The answer to e^{x^2+1}=5e^{-x} is x=(-1+sqrt(4ln(5)-3))/2 ,x=(-1-sqrt(4ln(5)-3))/2

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

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

x = \frac{- 1 + 4 ln ( 5 ) - 3}{2}, x = \frac{- 1 - 4 ln ( 5 ) - 3}{2}

Solution steps

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

Apply exponent rules

x^{2} + 1 = ln (5) - x

Solve

x^{2} + 1 = ln (5) - x : x = \frac{- 1 + 4 ln ( 5 ) - 3}{2}, x = \frac{- 1 - 4 ln ( 5 ) - 3}{2}

x = \frac{- 1 + 4 ln ( 5 ) - 3}{2}, x = \frac{- 1 - 4 ln ( 5 ) - 3}{2}

x^{5} = 5^{x}

4^{x + 1} = 64

2^{2 x + 1} = 4

e^{x} = - 3

(\frac{1}{4})^{4 x} = 0.25

What is the answer to e^{x^2+1}=5e^{-x} ?
The answer to e^{x^2+1}=5e^{-x} is x=(-1+sqrt(4ln(5)-3))/2 ,x=(-1-sqrt(4ln(5)-3))/2