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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?

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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!

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

Learn how to find the logarithm \( \log_{10} \left( \frac{1}{10000} \right) \) with a step-by-step solution. This problem uses key logarithmic concepts and properties, such as the logarithmic identity. Suitable for high school students in Grades 10-12.

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