The problem here is to find the logarithm:

$\log_{10} \left( \frac{1}{10000} \right)$

Solution:

1. Rewrite the fraction in terms of powers of 10: $\frac{1}{10000} = 10^{-4}$

2. Substitute $10^{-4}$ into the logarithmic expression: $\log_{10} (10^{-4})$

3. Using the property $\log_b(b^x) = x$, we get: $\log_{10} (10^{-4}) = -4$

Answer:

$\log_{10} \left( \frac{1}{10000} \right) = -4$

Would you like further explanation on logarithmic properties?

Here are some related questions for practice:

1. What is $\log_{10}(0.001)$?
2. Find $\log_{10} \left(\frac{1}{1000}\right)$.
3. Solve $\log_{10}(10^5)$.
4. What is the value of $\log_{10}(100)$?
5. Calculate $\log_{10}(0.1)$.

Tip: Remember, $\log_{10}(10^x) = x$ is a key property for solving these types of problems quickly!