What is the answer to e^{(x^2+4x-2)}=16 ?

The answer to e^{(x^2+4x-2)}=16 is x=(-4+sqrt(16ln(2)+24))/2 ,x=(-4-sqrt(16ln(2)+24))/2

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e^{(x^2+4x-2)}=16

e^{(x^{2} + 4 x - 2)} = 16

x = \frac{- 4 + 16 ln ( 2 ) + 24}{2}, x = \frac{- 4 - 16 ln ( 2 ) + 24}{2}

Decimal Notation

x = 0.96185 \dots, x = - 4.96185 \dots

Solution steps

e^{(x^{2} + 4 x - 2)} = 16

Apply exponent rules

x^{2} + 4 x - 2 = ln (16)

Solve

x^{2} + 4 x - 2 = ln (16) : x = \frac{- 4 + 16 ln ( 2 ) + 24}{2}, x = \frac{- 4 - 16 ln ( 2 ) + 24}{2}

x = \frac{- 4 + 16 ln ( 2 ) + 24}{2}, x = \frac{- 4 - 16 ln ( 2 ) + 24}{2}

4^{- 4 x} = 25

5^{8} \cdot 5^{4} = (125)^{x}

2^{4 x - 1} = 1

y, x = 1 + y + e^{y}

e^{4 x} = 32

What is the answer to e^{(x^2+4x-2)}=16 ?
The answer to e^{(x^2+4x-2)}=16 is x=(-4+sqrt(16ln(2)+24))/2 ,x=(-4-sqrt(16ln(2)+24))/2