Final answer:
The relative ages of igneous rocks can be most accurately determined through radiometric dating. Other methods like carbon dating, index fossils, and tree-ring dating are less applicable or ineffective for dating igneous rocks since they are either intended for organic materials or rely on different conditions than those provided by igneous formations.
Step-by-step explanation:
To determine the relative ages of igneous rocks, geologists can use various methods. One effective way to accomplish this is through radiometric dating, which is based on the decay of radioactive isotopes within the rocks. Processes like carbon dating, index fossil correlation, and tree-ring dating also provide insight into geological history but have different applications or limitations regarding igneous rocks.
Carbon dating is generally used for dating organic materials and is effective up to about 50,000 years, making it less applicable for most igneous rocks which are often much older. Index fossils are used in relative dating to identify the relative ages of sedimentary rocks rather than igneous rocks. Tree-ring dating, or dendrochronology, can provide precise years for events, but it's applicable to woody plants and therefore not used directly with igneous rocks.
Therefore, the most accurate method for dating igneous rocks is radiometric dating. This is because igneous rocks are formed from the cooling and solidification of magma or lava and can be dated by measuring the naturally occurring radioactive isotopes they contain.