What is the value of log₃ (1/27) in terms of an exponent?

To solve the equation ( log_3 left( frac{1}{27} right) = -3 ), we can use the definition of logarithms.

The equation states that ( log_3 left( frac{1}{27} right) = -3 ) means that ( 3^{-3} = frac{1}{27} ).

Now let’s evaluate ( 3^{-3} ):

– ( 3^{-3} = frac{1}{3^3} = frac{1}{27} ).

Since both sides of the equation are equal, the statement is true.

In summary, ( log_3 left( frac{1}{27} right) = -3 ) is correct because raising 3 to the power of -3 indeed equals ( frac{1}{27} ).

If you have more questions or would like deeper explanations on logarithms or another topic, feel free to ask!