To convert the equation \( 11^2 = \frac{1}{121} \) into a logarithmic equation, we can start by analyzing both sides of the equation.
First, we know that \( 121 = 11^2 \), which implies that \( \frac{1}{121} = 11^{-2} \). Thus, we can rewrite the original equation as:
\[ 11^2 = 11^{-2} \]
In logarithmic form, the equation \( a^b = c \) can be expressed as \( b = \log_a(c) \). Here, we can express the equation \( 11^2 = 11^{-2} \) as:
\[ 2 = \log_{11}(11^{-2}) \]
So the logarithmic equation corresponding to the original statement is:
\[ 2 = \log_{11}\left(\frac{1}{121}\right) \]
Alternatively, you can express it directly in terms of logarithms of numbers, if you prefer:
\[ \log_{11}(1) - \log_{11}(121) = 2 \]
This provides two valid transformations based on how you want to express the logarithmic equation.