What is the answer to 4^{-1/x}= 1/2 ?

The answer to 4^{-1/x}= 1/2 is x=2

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4^{-1/x}= 1/2

4^{- \frac{1}{x}} = \frac{1}{2}

x = 2

Solution steps

4^{- \frac{1}{x}} = \frac{1}{2}

Multiply both sides by

2

4^{- \frac{1}{x}} \cdot 2 = \frac{1}{2} \cdot 2

Simplify

4^{- \frac{1}{x}} \cdot 2 = 1

Divide both sides by

2

4^{- \frac{1}{x}} = \frac{1}{2}

Apply exponent rules

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

Solve

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

x = 2

Verify Solutions:

x = 2

True

The solution is

x = 2

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