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

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