Solve for x (1/2)^x=8

Problem

(1/2)x=8

Solution

1. Rewrite the fraction on the left side using a negative exponent.

(1/2)x=(2(−1))x

2. Apply the power of a power rule to simplify the left side.

(2(−1))x=2(−x)

3. Express the right side as a power of 2.

8=2

4. Equate the exponents since the bases are now the same.

−x=3

5. Solve for x by multiplying both sides by −1

x=−3

Final Answer

(1/2)x=8⇒x=−3

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