1. **Problem statement:** Given $\log_x 64 = 3$, find the value of $\log_x 8$. 2. **Recall the definition of logarithm:** If $\log_a b = c$, then $a^c = b$. 3. From the given equation $\log_x 64 = 3$, we rewrite it as: $$x^3 = 64$$ 4. Solve for $x$: Since $64 = 4^3$, we have: $$x^3 = 4^3 \implies x = 4$$ 5. Now, find $\log_x 8$ which is $\log_4 8$. 6. Express 8 in terms of base 4: $$8 = 2^3$$ 7. Use change of base formula or express both in base 2: $$\log_4 8 = \frac{\log_2 8}{\log_2 4} = \frac{3}{2}$$ **Final answer:** $$\log_x 8 = \frac{3}{2}$$