**Core Concept**
Cephalosporins are a class of beta-lactam antibiotics that exhibit varying degrees of renal excretion. The pharmacokinetics of cephalosporins, particularly their clearance and half-life, can be affected by renal impairment, necessitating dose adjustments to maintain efficacy and prevent toxicity.

**Why the Correct Answer is Right**
Ceftriaxone is a third-generation cephalosporin with a unique pharmacokinetic profile that allows it to be effectively cleared from the body through the biliary system, rather than the kidneys. This characteristic enables ceftriaxone to be administered without dose adjustments in patients with renal impairment. Ceftriaxone's long half-life (approximately 8 hours) and extensive biliary excretion make it an ideal choice for patients with compromised renal function.

**Why Each Wrong Option is Incorrect**
* **Option A:** Cephalothin is a first-generation cephalosporin that is primarily excreted by the kidneys. Renal impairment would necessitate dose reduction to prevent accumulation and toxicity.
* **Option B:** Cefazolin is a first-generation cephalosporin that is also excreted mainly by the kidneys. Dose adjustment is required in patients with renal impairment to avoid nephrotoxicity.
* **Option C:** Cefotaxime is a third-generation cephalosporin, but it is primarily excreted by the kidneys. While it may not require as frequent dose adjustments as other cephalosporins, renal impairment would still necessitate some degree of dose reduction.

**Clinical Pearl / High-Yield Fact**
When managing patients with renal impairment, it is essential to consider the pharmacokinetics of the medication, including its clearance, half-life, and route of excretion. This knowledge will help guide dose adjustments and minimize the risk of adverse effects.

**Correct Answer: C. Ceftriaxone**