Exponential and Logarithmic Functions Change of base for logarithms: Problem type 1 Use the change of base formula to compute $\log _{9} 8$. Round your answer to the nearest thousandth.

Step 1 ：The change of base formula for logarithms is given by: \[\log_b a = \frac{\log_c a}{\log_c b}\] where c is the new base.

Step 2 ：We can use any base for c, but for simplicity, we'll use base e (natural logarithm).

Step 3 ：So, to compute \(\log_9 8\), we can use the change of base formula to convert it to base e: \[\log_9 8 = \frac{\log_e 8}{\log_e 9}\]

Step 4 ：After calculating, we get the result as 0.946

Step 5 ：The result makes sense. The logarithm of 8 with base 9 is less than 1 because 9 to the power of 1 is 9, which is greater than 8. Therefore, the logarithm of 8 with base 9 should be less than 1. The computed result of 0.946 is consistent with this expectation.

Step 6 ：Final Answer: \(\boxed{0.946}\)