What is the answer to (1/2)^x=2^{x+3} ?

The answer to (1/2)^x=2^{x+3} is x=-3/2

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(1/2)^x=2^{x+3}

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

x = - \frac{3}{2}

Solution steps

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

Apply exponent rules

- x = x + 3

Solve

- x = x + 3 : x = - \frac{3}{2}

x = - \frac{3}{2}

2^{x - 1} + 20 = 3 (2^{x})

\frac{13}{2 ^{x}} = 3^{x - 5}

2^{3 x + 5} = 32 (8)^{x}

x, e^{x} = 1

2^{4 x} = 127