To simplify \( 2\log(9) - 3\log(x) \), we can use the properties of logarithms.

### Step-by-Step Solution

1. **Use the Power Rule**: The power rule of logarithms states that \( a \log(b) = \log(b^a) \).
   \[
   2\log(9) = \log(9^2) = \log(81)
   \]
   and
   \[
   3\log(x) = \log(x^3).
   \]

   Substituting these into the expression, we get:
   \[
   \log(81) - \log(x^3).
   \]

2. **Use the Quotient Rule**: The quotient rule of logarithms states that \( \log(a) - \log(b) = \log\left(\frac{a}{b}\right) \).
   \[
   \log(81) - \log(x^3) = \log\left(\frac{81}{x^3}\right).
   \]

### Final Answer
The simplified form is:
\[
\log\left(\frac{81}{x^3}\right).
\]

Would you like a deeper explanation, or do you have any questions?

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### Related Questions

1. How would you simplify \( 3\log(x) - 2\log(y) \)?
2. What is the simplified form of \( \log(a^2) - \log(b^2) \)?
3. How can you rewrite \( \log(x^2) + 2\log(y) \)?
4. If \( \log(x) = 2 \), what is \( 2\log(x) - \log(x^2) \)?
5. How would you simplify \( 4\log(5) - \log(x) \)?

### Tip
Remember, the power rule \( a\log(b) = \log(b^a) \) is very helpful for simplifying expressions with coefficients in front of logs.

Discover how to simplify the expression 2log(9) - 3log(x) using logarithmic properties like the Power Rule and Quotient Rule. This step-by-step guide is designed for high school students in Grades 9-12.

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