The Earth's metallic core exists under extreme pressure (136–364 GPa) and temperature (4000–6000 K) conditions. Under these conditions, the core is almost molten, i.e., the liquid outer core occupies 95% of the entire volume. The core primarily consists of iron (Fe) alloyed with lighter elements such as hydrogen (H), carbon (C), nitrogen (N), oxygen (O), silicon (Si), phosphorus (P), and sulfur (S) [1,2]. Determining the core's chemical composition is crucial for understanding planetary formation processes and current core dynamics. However, the nature of the core is still controversial. The direct observational data are limited to seismologically derived sound velocity and density measurements. This makes the elastic properties of liquid Fe alloys under high pressure and temperature (P-T) conditions essential for constraining core composition. We have employed meV-resolution inelastic X-ray scattering (IXS) measurements combined with the laser-heated diamond-anvil cell (LH-DAC) technique at BL35XU [3] and BL43LXU [4,5] beamlines of the SPring-8 synchrotron facility in Japan. Using LH-DAC to generate extreme conditions, we measure longitudinal acoustic phonon modes in liquid alloys through IXS. The P-wave velocity is determined via dispersion relations of these phonon modes. Previously, we have achieved sound velocity measurements for liquid Fe alloys with C, Si, P, and S up to 70 GPa and 3200 K [6-9], while recent advancements now extend these measurements to 100 GPa and 3000 K. Our results exhibited that each element has a characteristic effect on the elastic properties including P-wave velocity of liquid Fe, which can be due to the different property on the modification of the structure and chemical bonding in liquid Fe. Comparing the results with seismological observations, we also constrained the abundance of each component in the Earth's outer core. In this talk, I will discuss our developments in IXS measurements under extreme P-T conditions and their application to studying the chemical composition of the Earth's core. References 1. Stevenson, Science 214, 611-619 (1981) 2. Hirose et al. Annual Rev. Earth Planet. Sci. 41, 657-691 (2013). 3. Baron et al. Phys. Chem. Solids 61, 461–465 (2000). 4. Baron, SPring-8 Inf. Newsl. 15, 14–19 (2010). 5. Baron et al. AIP Conf. Proc. 2054, 020002 (2019). 6. Nakajima et al. Nat. Commun., 6, 8942 (2015). 7. Nakajima et al. J. Geophys. Res., 125, e2020JB019399 (2020). 8. Kuwayama et al. Phys. Rev. Lett. 124, 165701 (2020). 9. Kinoshita et al. Phys. Stat. Sol. B 257, 2000171 (2020).