Evaluate log base 3 of 1/81

Problem

(log_3)(1/81)

Solution

1. Rewrite the fraction as a power of the denominator.

1/81=81(−1)

2. Express the number 81 as a power of the base 3.

81=3

3. Substitute this power back into the expression using the power of a power rule.

1/81=(3)(−1)=3(−4)

4. Apply the logarithm property (log_b)(bx)=x to evaluate the expression.

(log_3)(3(−4))=−4

Final Answer

(log_3)(1/81)=−4

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