Evaluate log base 3 of 1/27

Problem

(log_3)(1/27)

Solution

1. Identify the base and the argument of the logarithm. The base is 3 and the argument is 1/27

2. Rewrite the argument as a power of the base. Since 27=3 the fraction can be written using a negative exponent.

1/27=1/3

3. Apply the rule for negative exponents, which states that 1/(an)=a(−n)

1/3=3(−3)

4. Substitute the power back into the logarithmic expression.

(log_3)(3(−3))

5. Use the property of logarithms (log_b)(bx)=x to evaluate the expression.

(log_3)(3(−3))=−3

Final Answer

(log_3)(1/27)=−3

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