Evaluate \(\log_{0.25} 8\)

We can use the change of base formula to evaluate \(\log_{0.25} 8\). The change of base formula states that for any positive numbers \(a\), \(b\), and \(c\) with \(a \neq 1\), we have: \(\log_{a} b = \frac{\log_{c} b}{\log_{c} a}\) In this case, we can choose any base we like, but it is convenient to use base 2 because 8 and 0.25 are powers of 2. So, we can rewrite the expression as: \(\log_{0.25} 8 = \frac{\log_{2} 8}{\log_{2} 0.25}\) Now, we can evaluate the logarithms on the right-hand side using the rules of logarithms. We know that \(2^{3} = 8\) and \(2^{-2} = 0.25\), so we have: \(\log_{2} 8 = 3\) and \(\log_{2} 0.25 = -2\) Substituting these values into the equation above, we get: \(\log_{0.25} 8 = \frac{3}{-2} = -\frac{3}{2}\) Therefore, the value of \(\log_{0.25} 8\) is \(-\frac{3}{2}\). Hence, the answer is \(-\frac{3}{2}\).