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

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

24 3^{x + 2} \cdot 9^{2 x - 1} = 9

200 = 100 (1 + \frac{8}{100})^{x}

8^{x - 3} = 6 4^{3 - x}

\frac{5 ^{x + 1} - 20}{10 + 5 ^{x}} = 3

10 + 2 \cdot 2^{x} = 18

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)