Final answer:
The expression log9 9 evaluates to 1 because any logarithm of a number to its own base is always 1.
Step-by-step explanation:
The student has asked to evaluate the expression log9 9. The logarithm of a number to its own base is always 1, because the base raised to the power of 1 is the number itself. In other words, since 9 raised to the power of 1 is 9, log9 9 equals 1.
To calculate this without a calculator, you apply the basic logarithm rule: logb a = c if and only if bc = a. For this question, the base b is 9 and the number a is also 9. Thus, we are looking for the exponent c that makes 9c = 9. Since any number raised to the power of 1 is itself, the answer is clearly c = 1, or log9 9 = 1.