To convert the exponential equation to logarithmic form, we start with the exponential expression given by \( 3^{-2} = \frac{1}{9} \).
In logarithmic form, this can be expressed as:
\[ \log_3 \left( \frac{1}{9} \right) = -2 \]
So your original statement \( \log_3 \frac{1}{9} = -2 \) is already in logarithmic form. The corresponding exponential equation is:
\[ 3^{-2} = \frac{1}{9} \]
Thus, the logarithmic form of the original exponential equation \( 3^? = \frac{1}{9} \) is:
\[ \log_3 \left( \frac{1}{9} \right) = ? \]
And since we know the exponent is \(-2\), we have:
\[ \log_3 \left( \frac{1}{9} \right) = -2 \]
1 answer