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.