Evaluate log base 3 of 1/9

Problem

(log_3)(1/9)

Solution

1. Identify the base and the argument of the logarithm. The base is 3 and the argument is 1/9

2. Rewrite the argument as a power of the base. Since 9=3 the fraction can be written using a negative exponent.

1/9=1/3

1/3=3(−2)

3. Substitute the power back into the logarithmic expression.

(log_3)(3(−2))

4. Apply the logarithm power rule, which states that (log_b)(bx)=x

(log_3)(3(−2))=−2

Final Answer

(log_3)(1/9)=−2

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