Which of the following is an approximation to six decimal places of log subscript 9 baseline 1 comma 620?

Question

(1 point)
Responses

2.255273
2.255273

3.209515
3.209515

3.363417
3.363417

7.390181

Answer 1

To find the approximation of \( \log_9(1620) \), we can use the change of base formula:

\[ \log_9(1620) = \frac{\log_{10}(1620)}{\log_{10}(9)} \]

First, we calculate \( \log_{10}(1620) \) and \( \log_{10}(9) \):

1. \( \log_{10}(1620) \approx 3.209515 \) (using a calculator)
2. \( \log_{10}(9) \approx 0.954243 \) (since \( 9 = 3^2 \) and \( \log_{10}(3) \approx 0.477121 \))

Now substitute these into the change of base formula:

\[ \log_9(1620) \approx \frac{3.209515}{0.954243} \approx 3.363417 \]

Rounding to six decimal places, we find that:

\[ \log_9(1620) \approx 3.363417 \]

Thus, the correct answer is:

3.363417