Problem
Which of the following logarithmic equations is equivalent to the statement $3^{-3}=\frac{1}{27} ?$ $\log _{3}(3)=\frac{1}{27}$ $\log _{3}(27)=-3$ $\log _{-3}\left(\frac{1}{27}\right)=3$ $\log _{3}\left(\frac{1}{27}\right)=-3$ $27 \cdot \log (3)=-3$
Solution
Step 1 ：We are given the equation $3^{-3}=\frac{1}{27}$ and asked to convert it into logarithmic form.
Step 2 ：The logarithmic form of the equation $3^{-3}=\frac{1}{27}$ is $\log_{3}\left(\frac{1}{27}\right)=-3$. This is because the logarithm base $3$ of $1/27$ is $-3$, as $3$ raised to the power of $-3$ equals $1/27$.
Step 3 ：Final Answer: \(\boxed{\log_{3}\left(\frac{1}{27}\right)=-3}\)
