Final answer:
The evaluation of log_9(243) is 3, because 243 can be expressed as 9 cubed, and when the bases are the same in a logarithmic expression, the result is the exponent.
Step-by-step explanation:
The student has asked to evaluate log9(243). To solve this, we need to understand that a logarithm is asking what power we need to raise the base (in this case, 9) to get the number inside the log (here, 243).
We can write 243 as 92 because 9 squared is 81 and 81 multiplied by 3 (another 9) equals 243. Thus, 243 is 92 * 9 = 93.
The equation now simplifies to log9(93). Since the base of the logarithm and the base inside the log are the same, the answer is just the exponent, which is 3. So, log9(243) = 3.