(8.) $$ \log _{4} x-\log _{4} 8=3 $$

Question

UpStudy AI · Accepted Answer

1. Rewrite the equation:
   $$
   \log_{4}x - \log_{4}8 = 3
   $$

2. Use the logarithmic property:
   $$
   \log_{4}\left(\frac{x}{8}\right) = 3
   $$

3. Convert the logarithmic form to exponential form:
   $$
   \frac{x}{8} = 4^3
   $$

4. Calculate $$4^3$$:
   $$
   4^3 = 64
   $$

5. Solve for $$x$$:
   $$
   \frac{x}{8} = 64 \quad \Rightarrow \quad x = 8 \times 64 = 512
   $$

The solution is $$ x = 512 $$.
$$ x = 512 $$

(8.)