Use the like bases property to solve the equation \( \left(\frac{1}{2}\right)^{x}=8 \) \( x=\square \) Question Help: Vided

To solve the equation \( \left(\frac{1}{2}\right)^{x} = 8 \) using the like bases property, we need to express both sides of the equation with the same base. 1. **Identify the bases**: The left side has a base of \( \frac{1}{2} \), and the right side is \( 8 \). We can express \( 8 \) as a power of \( \frac{1}{2} \). 2. **Convert \( 8 \) to a power of \( \frac{1}{2} \)**: \[ 8 = 2^3 \] Since \( \frac{1}{2} = 2^{-1} \), we can rewrite \( 8 \) as: \[ 8 = (2^{-1})^{-3} = \left(\frac{1}{2}\right)^{-3} \] 3. **Rewrite the equation**: Now we can rewrite the original equation: \[ \left(\frac{1}{2}\right)^{x} = \left(\frac{1}{2}\right)^{-3} \] 4. **Set the exponents equal**: Since the bases are the same, we can set the exponents equal to each other: \[ x = -3 \] Thus, the solution to the equation is: \[ x = -3 \]