Find the logarithm using the change of base formula. \[ \log _{8} 40 \] $\log _{8} 40=\square$ (Round to four decimal places as needed.)

Step 1 ：We are asked to find the value of \(\log_8 40\).

Step 2 ：We can use the change of base formula to change the base from 8 to 10 (since base 10 is the most common base and is easy to calculate).

Step 3 ：The change of base formula is \(\log_b a = \frac{\log_k a}{\log_k b}\), where a is the number we are taking the logarithm of, b is the base of the logarithm, and k is the new base.

Step 4 ：In this case, a = 40, b = 8, and k = 10.

Step 5 ：Using the formula, we get \(\log_8 40 = \frac{\log_{10} 40}{\log_{10} 8}\).

Step 6 ：Calculating the values, we get \(\log_8 40 = \frac{1.6020599913279625}{0.9030899869919435} = 1.773976031629121\).

Step 7 ：Rounding to four decimal places, the value of \(\log_8 40\) is approximately 1.7740.

Step 8 ：Final Answer: The value of \(\log_8 40\) is \(\boxed{1.7740}\) when rounded to four decimal places.