Find the logarithm using the change of base formula.
$${\log }_{8}40$$
${\log }_{8}40=◻$
(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 $\boxed{{\displaystyle 1.7740}}$ when rounded to four decimal places.