Final answer:
To approximate the base 9 logarithm of 1620, we use the change of base formula with common logarithms. The calculations show that the correct approximation within given options does not match our result, suggesting there might be an error in the question or options presented.
Step-by-step explanation:
The subject of this question is logarithms, and it is addressed towards students in high school level mathematics. To find the logarithm of 1620 to the base 9, we will use the change of base formula which states that logb(x) = log(x) / log(b), where log signifies a logarithm (commonly base 10 for calculators).
First, we calculate the logarithm of 1620 and 9 using the base 10 (as calculators typically have buttons for log to the base 10). Then we will divide the logarithm of 1620 by the logarithm of 9 to get our answer. After calculating this on a calculator, we get the following:
- log(1620) ≈ 3.209515
- log(9) ≈ 0.954242
- log9(1620) ≈ 3.209515 / 0.954242 ≈ 3.362215
However, none of the provided options match exactly the result we calculated. There might have been a mistake in the options or in the base provided for the logarithm since a base 10 logarithm was used for calculations. If a different base or method was meant to be used, that may explain the discrepancy. In the situation provided, we do not have enough information to determine the correct option and might need to revisit the question for any mistakes or assumptions we've missed.