Question: (\[ 28^{-2} = \frac{1}{784} \] \[ \log_{28} \frac{1}{784} = -2 \] \[ \log_{-2}…

\(\[ 28^{-2} = \frac{1}{784} \]

\[ \log_{28} \frac{1}{784} = -2 \]

\[ \log_{-2} \frac{1}{784} = 28 \]

\[ \log_{28} -2 = \frac{1}{784} \]

\[ \log_{\frac{1}{784}} 28 = -2 \]\)

Solution

We need to determine which option matches the exponential equation: \[ 28^{-2} = \frac{1}{784} \] Given this, let’s analyze each option: 1. \(\log_{28} \frac{1}{784} = -2\) This matches because the equation \(\log_{b} a = c\) implies that \(b^c = a\). Here, \(28^{-2} = \frac{1}{784}\). 2. \(\log_{-2} \frac{1}{784} = 28\) This is incorrect because the base of a logarithm cannot be negative. 3. \(\log_{28} -2 = \frac{1}{784}\) This is incorrect because \(\log_{28} -2\) is undefined (logarithms are not defined for negative numbers). 4. \(\log_{\frac{1}{784}} 28 = -2\) This would imply that \(\left(\frac{1}{784}\right)^{-2} = 28\), which is not true. Thus, the correct answer is: \[ \log_{28} \frac{1}{784} = -2 \]