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

The answer to solvefor x,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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solvefor x,e^{x^2+1}=5e^{-x}

solve for

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

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

Decimal Notation

x = 0.42705 \dots, x = - 1.42705 \dots

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}

4^{3 x - 15} - 64 = 0

2^{x^{2}} = 8

64 = 3 2^{- x + 2}

ln (e^{x}) = 15

ln (e^{x}) = 28

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