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

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

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

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

x = \frac{2 ln ( 2 )}{ln ( 2 e )} + 2, x = - \frac{2 ln ( 2 )}{ln ( 2 e )} + 2

Decimal Notation

x = 1.67891 \dots, x = - 1.67891 \dots

Solution steps

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

Apply exponent rules

(x^{2} - 2) ln (2 e) = ln (4)

Solve

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

x = \frac{2 ln ( 2 )}{ln ( 2 e )} + 2, x = - \frac{2 ln ( 2 )}{ln ( 2 e )} + 2

- 4 \cdot 3^{6 w} = - 1750

x, e = e^{x y}

(\frac{1}{4})^{x} = 64

\frac{( 2 ^{x} - 2 ^{- x} )}{3} = 4

e^{6 x} = e^{2 x + 1}

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