The question asks to find the value of the logarithm:

$\log_{10}(10,000).$

Step-by-step Solution:

1. Recall the logarithmic definition: $\log_b(x) = y \quad \text{if and only if} \quad b^y = x.$

2. In this case:

   • Base ($b$) = $10$,
   • Argument ($x$) = $10,000$.

3. Rewrite $10,000$ as a power of 10: $10,000 = 10^4.$

4. By the definition of logarithms: $\log_{10}(10,000) = 4.$

Final Answer:

$\boxed{4}$

Would you like a more detailed explanation or help with similar logarithmic problems?

Related Questions:

1. What is $\log_{10}(1,000)$?
2. How do you simplify $\log_{10}(0.01)$?
3. What does $\log_{10}(x)$ mean graphically on a coordinate plane?
4. How do you solve $10^x = 1,000,000$ using logarithms?
5. Can you explain the difference between natural logarithms ($\ln(x)$) and base-10 logarithms?

Tip:

When dealing with base-10 logarithms ($\log_{10}$), remember they are often called "common logarithms" and are used extensively in sciences and engineering.