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.