Final answer:
The value of log₉ 729 is 3, because 9 raised to the power of 3 is equal to 729.
Step-by-step explanation:
To find the value of log₉ 729, we need to determine the power to which the base 9 must be raised to obtain 729. This can be represented as 9x = 729.
First, we should recognize that 729 is a power of 9:
91 = 9
92 = 81
93 = 729
With this pattern, we can see that 9 raised to the third power equals 729. Therefore, the value of log₉ 729 is 3.