Evaluate log base 3 of 1/3

Problem

(log_3)(1/3)

Solution

1. Identify the logarithmic expression and rewrite the argument as a power of the base.

2. Apply the property of negative exponents, which states that 1/a=a(−1)

1/3=3(−1)

3. Substitute the power back into the logarithm.

(log_3)(3(−1))

4. Apply the logarithm power rule (log_b)(bx)=x

(log_3)(3(−1))=−1

Final Answer

(log_3)(1/3)=−1

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