What is the answer to 2^{3x}=0.5^{2x^2-2} ?

The answer to 2^{3x}=0.5^{2x^2-2} is x=-2,x= 1/2

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2^{3x}=0.5^{2x^2-2}

2^{3 x} = 0. 5^{2 x^{2} - 2}

x = - 2, x = \frac{1}{2}

Decimal Notation

x = - 2, x = 0.5

Solution steps

2^{3 x} = 0. 5^{2 x^{2} - 2}

2^{3 x} = (\frac{1}{2})^{2 x^{2} - 2}

Apply exponent rules

3 x = - (2 x^{2} - 2)

Solve

3 x = - (2 x^{2} - 2) : x = - 2, x = \frac{1}{2}

x = - 2, x = \frac{1}{2}

8^{x} - 2 = 0

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

3^{5 x - 2} = 4

5^{\frac{12}{t ^{2}}} = 18

1 1^{x^{2} - 3 x + 2} = 121

What is the answer to 2^{3x}=0.5^{2x^2-2} ?
The answer to 2^{3x}=0.5^{2x^2-2} is x=-2,x= 1/2
Solve for x: 2^{3x}=0.5^{2x^2-2}
The solution is x=-2,x= 1/2