log₃ (1/27) = -3
-³ = 1/27
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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!