Which of the following logarithmic equations is equivalent to the statement $3^{-3}=\frac{1}{27} ?$
$\log _{3}(3)=\frac{1}{27}$
$\log _{3}(27)=-3$
$\log _{-3}\left(\frac{1}{27}\right)=3$
$\log _{3}\left(\frac{1}{27}\right)=-3$
$27 \cdot \log (3)=-3$

Answer

Expert–verified

Hide Steps

Answer

Final Answer: $\boxed{\log_{3}\left(\frac{1}{27}\right)=-3}$

Steps

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: $\boxed{\log_{3}\left(\frac{1}{27}\right)=-3}$

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$

Answer

Popular Problems

Which of the following logarithmic equations is equivalent to the statement $3^{-3}=\frac{1}{27} ?$
$\log _{3}(3)=\frac{1}{27}$
$\log _{3}(27)=-3$
$\log _{-3}\left(\frac{1}{27}\right)=3$
$\log _{3}\left(\frac{1}{27}\right)=-3$
$27 \cdot \log (3)=-3$