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 \( \left(\frac{1}{2}\right)^{x}=8 \), start by rewriting \( 8 \) with a base of \( \frac{1}{2} \). Since \( 8 = 2^3 \) and \( \frac{1}{2} = 2^{-1} \), you can rewrite \( 8 \) as \( \left(2^{-1}\right)^{-3} = \left(\frac{1}{2}\right)^{-3} \). Now, your equation looks like \( \left(\frac{1}{2}\right)^{x} = \left(\frac{1}{2}\right)^{-3} \). Since the bases are the same, you can set the exponents equal to each other: \( x = -3 \). Now you have: \( x = -3 \) But what does this mean? You've just discovered that to get from \( \frac{1}{2} \) to \( 8 \), you need to flip the fraction and raise it to a power. It’s like flipping a switch; if the number is less than 1, it'll escalate quickly in the opposite direction to create a larger value!