Final answer:
The evaluation of log base 3 of 1/3 gives a result of -1, as 1/3 is equivalent to 3 raised to the power of -1.
Step-by-step explanation:
The question is asking to evaluate log base 3 of 1/3. This can be interpreted as finding the exponent that 3 must be raised to in order to yield 1/3. Since 1/3 is the same as 3-1, we can see that the exponent is -1. So, the logarithm is simply the exponent, which in this case is -1.
Using the property that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number (logb(np) = p · logb(n)), we apply it here:
log3(3-1) = -1 · log3(3) = -1 · 1 = -1
Thus, log base 3 of 1/3 is equal to -1.