To determine which of the logarithmic expressions is undefined, we need to remember that logarithms are only defined for positive arguments. This means we cannot take the logarithm of a negative number or zero.
Let's analyze each expression:
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log₃(−9): This expression is undefined because the argument (−9) is negative.
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log₃(27): This expression is defined because 27 is a positive number.
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log₀.25(64): This expression is defined because 64 is a positive number.
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log₂.56.25: This expression is defined because 2.56 is a positive number (approximating this means it's between 2 and 3), and 0.25 is also a positive number.
Given this analysis, the expression that is undefined is:
log₃(−9).