Question

Write the exponential equation in logarithmic form.
log3 1/9 = -2
3^? = 1/9

Answer 1

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:

\[
\log_3 \left( \frac{1}{9} \right) = -2
\]