Find the solution. Select the correct next step. $$ \log _{4}(8 x)-\log _{4}(x-7)=3 $$ $$ \log _{4}\left(\frac{8 x}{x-7}\right)=3 \quad \log _{4}(8 x(x-7))=3 \quad \log _{4}\left(\frac{x-7}{8 x}\right)=3 $$

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
\log_{4}(8x) - \log_{4}(x-7) = 3
$$

**Step 1: Apply the Quotient Rule for Logarithms**

The quotient rule states that $$\log_b(A) - \log_b(B) = \log_b\left(\frac{A}{B}\right)$$. Applying this rule to the given equation:

$$
\log_{4}\left(\frac{8x}{x-7}\right) = 3
$$

**Answer:**

$$
\log_{4}\left(\frac{8 x}{x-7}\right)=3
$$

**This corresponds to the first option provided.**

Answer: 
$$
\log_{4}\left(\frac{8 x}{x-7}\right)=3
$$
$$ \log_{4}\left(\frac{8x}{x-7}\right) = 3 $$

Find the solution.
Select the correct next step.

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