We are tasked with solving the equation \( 2 \log 8 - 3 \log 9 = x \).

### Step-by-Step Solution:

#### 1. Apply the logarithmic property:
\[
a \log b = \log b^a
\]
Thus, we can rewrite the equation as:

\[
\log 8^2 - \log 9^3 = x
\]

#### 2. Simplify the exponents:
\[
\log 64 - \log 729 = x
\]

#### 3. Use the logarithmic subtraction rule:
\[
\log a - \log b = \log \left( \frac{a}{b} \right)
\]
Therefore, the equation becomes:

\[
\log \left( \frac{64}{729} \right) = x
\]

#### 4. Calculate the fraction:
\[
\frac{64}{729} \approx 0.0878
\]

#### 5. Find the logarithm:
\[
x = \log (0.0878) \approx -1.057
\]

Thus, the solution is:
\[
x \approx -1.057
\]

Would you like more details on any of the steps?

### Related Questions:
1. How do logarithmic rules help simplify complex equations?
2. What are common properties of logarithms?
3. How can we calculate logarithms of non-standard values without a calculator?
4. What is the importance of base-10 logarithms in real-life applications?
5. How does the subtraction rule for logarithms differ from multiplication?

#### Tip:
Remember that logarithms convert multiplication into addition and division into subtraction, which simplifies handling large numbers.

Learn how to solve the logarithmic equation ²Log 8 - ³Log 9 = x with a detailed step-by-step solution. This problem covers key logarithmic concepts, including exponentiation and subtraction rules. Suitable for students in Grades 9-12.

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