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The expression simplifies to:

\[
\frac{1}{24 \cdot \log(\log(10))} + \frac{\log(3)}{\log(10)} + 1
\]

Would you like further clarification or any additional details? Here are 5 related questions you might be interested in:

1. What is the approximate value of this expression?
2. How do logarithmic properties help simplify complex expressions?
3. Can we compute \(\log(\log(10))\) numerically?
4. How would this expression change if the logarithm base was different?
5. What are the real-world applications of such logarithmic expressions?

**Tip:** Logarithms are often used to simplify the handling of very large or small numbers, making them particularly useful in scientific and engineering fields.

log(30) - 1 / (48 * log(log(10))) + 1 / (16 * log(log(10)))?

Explore the step-by-step simplification of a logarithmic expression involving log(30), nested logarithms like log(log(10)), and fractional coefficients. This example covers key logarithmic concepts and theorems, ideal for students in Grades 10-12.

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