Express \( 5^{-2}=\frac{1}{25} \) in logarithmic form. \( \begin{array}{ll}\text { a. } \log _{\frac{1}{25}}(-2)=5 & \text { b. } \log _{\frac{1}{25}}(5)=-2 \\ \text { c. } \log _{5}\left(\frac{1}{25}\right)=-2 & \text { d. } \log _{5}(-2)=\frac{1}{25}\end{array} \)

To convert the expression \( 5^{-2} = \frac{1}{25} \) into logarithmic form, we remember that the logarithmic form of \( a^b = c \) is written as \( \log_{a}(c) = b \). Here, we can identify: - \( a = 5 \) - \( b = -2 \) - \( c = \frac{1}{25} \) Thus, in logarithmic form, this becomes: \[ \log_{5}\left(\frac{1}{25}\right) = -2 \] Looking at the options provided: - Option \( c \) is \( \log_{5}\left(\frac{1}{25}\right) = -2 \), which is the correct answer. So the answer is \( \log_{5}\left(\frac{1}{25}\right) = -2 \) from option **c**.