Termo geral da soma de infinitos termos: $|f(x) \cdot \frac{1}{4} \cdot \left(\frac{2}{3} \right)^{n-1}| = |f(x) \cdot \frac{3}{8} \cdot \left(\frac{2}{3} \right)^{n}|$. Temos: $\Large{\frac{3}{8}}$ $\cdot f(x)$ $\underbrace{ \cdot \displaystyle\sum_{n=1}^{\infty} {\left( \frac{2}{3}\right)^n}}_{2}$ $\leq$ $\Large{\frac{9}{4}}$ $\implies$ $f(x) \leq 3$ $\implies$ $|3-\log x| \leq 3$. Resolvamos a inequação modular:$$|3-\log x| \leq 3 \implies \log x \geq 0 \space \space \text{ou} \space \log x \leq 6$$Assim, $\boxed{10^0 \leq x \leq 10^6}$$$\text{Alternativa} \space \mathbb{(D)}$$