Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.
$$\log \left(\frac{\sqrt{u^2+v^2}}{100.000}\right)=◻$$

Step 1 ：The given expression is a logarithm of a fraction. We can use the properties of logarithms to simplify this expression. The logarithm of a fraction can be written as the difference of the logarithms of the numerator and the denominator.

Step 2 ：Also, the square root of a number is the same as raising that number to the 1/2 power. So, we can rewrite the square root in the numerator as a power of 1/2.

Step 3 ：Then, we can use the property of logarithms that allows us to bring the exponent out in front of the logarithm.

Step 4 ：Applying these steps, we get: $\frac{1}{2}\log (u^2+v^2)-\log (100000)$

Step 5 ：We know that $\log (100000)=5$, so we can simplify the expression further to get the final answer.

Step 6 ：$\boxed{{\displaystyle \frac{1}{2}\log (u^2+v^2)-5}}$